Selective deposition modeling method and apparatus for forming three-dimensional objects and supports

ABSTRACT

A variety of support structures and build styles for use in Rapid Prototyping and Manufacturing systems are described wherein particular emphasis is given to Thermal Stereolithography, Fused Deposition Modeling, and Selective Deposition Modeling systems, and wherein a 3D modeling system is presented which uses multijet dispensing and a single material for both object and support formation.

This application is a divisional of U.S. Ser. No. 09/252,512, filed Feb.18, 1999; which is a divisional of U.S. Ser. No. 08/722,335, filed Sep.27, 1996, now abandoned; which is a continuation-in-part of U.S. Ser.No. 08/534,813, filed Sep. 27, 1995, now abandoned.

FIELD OF THE INVENTION

This invention relates to techniques for forming three-dimensional (3D)objects and supporting those objects during formation; moreparticularly, it relates to techniques for use in Rapid Prototyping andManufacturing (RP&M) Systems; and most particularly to building andsupporting methods and apparatus for use in a Thermal Stereolithography(TSL) system, Fused Deposition Modeling (FDM) system, or other SelectiveDeposition Modeling (SDM) system.

BACKGROUND INFORMATION

Various approaches to automated or semi-automated three-dimensionalobject production or Rapid Prototyping & Manufacturing have becomeavailable in recent years, characterized in that each proceeds bybuilding up 3D objects from 3D computer data descriptive of the objectsin an additive manner from a plurality of formed and adhered laminae.These laminae are sometimes called object cross-sections, layers ofstructure, object layers, layers of the object, or simply layers (if thecontext makes it clear that solidified structure of appropriate shape isbeing referred to). Each lamina represents a cross-section of thethree-dimensional object. Typically lamina are formed and adhered to astack of previously formed and adhered laminae. In some RP&Mtechnologies, techniques have been proposed which deviate from a strictlayer-by-layer build up process wherein only a portion of an initiallamina is formed and prior to the formation of the remaining portion(s)of the initial lamina, at least one subsequent lamina is at leastpartially formed.

According to one such approach, a three-dimensional object is built upby applying successive layers of unsolidified, flowable material to aworking surface, and then selectively exposing the layers to synergisticstimulation in desired patterns, causing the layers to selectivelyharden into object laminae which adhere to previously-formed objectlaminae. In this approach, material is applied to the working surfaceboth to areas which will not become part of an object lamina, and toareas which will become part of an object lamina. Typical of thisapproach is Stereolithography (SL), as described in U.S. Pat. No.4,575,330, to Hull. According to one embodiment of Stereolithography,the synergistic stimulation is radiation from a UV laser, and thematerial is a photopolymer. Another example of this approach isSelective Laser Sintering (SLS), as described in U.S. Pat. No.4,863,538, to Deckard, in which the synergistic stimulation is IRradiation from a CO₂ laser and the material is a sinterable powder. Thisfirst approach may be termed photo-based stereolithography. A thirdexample is Three-Dimensional Printing (3DP) and Direct Shell ProductionCasting (DSPC), as described in U.S. Pat. Nos. 5,340,656 and 5,204,055,to Sachs, et al., in which the synergistic stimulation is a chemicalbinder (e.g. an adhesive), and the material is a powder consisting ofparticles which bind together upon selective application of the chemicalbinder.

According to a second such approach, an object is formed by successivelycutting object cross-sections having desired shapes and sizes out ofsheets of material to form object lamina. Typically in practice, thesheets of paper are stacked and adhered to previously cut sheets priorto their being cut, but cutting prior to stacking and adhesion ispossible. Typical of this approach is Laminated Object Manufacturing(LOM, as described in U.S. Pat. No. 4,752,352, to Feygin in which thematerial is paper, and the means for cutting the sheets into the desiredshapes and sizes is a CO₂ laser. U.S. Pat. No. 5,015,312 to Kinzie alsoaddresses building object with LOM techniques.

According to a third such approach, object laminae are formed byselectively depositing an unsolidified, flowable material onto a workingsurface in desired patterns in areas which will become part of an objectlaminae. After or during selective deposition, the selectively depositedmaterial is solidified to form a subsequent object lamina which isadhered to the previously-formed and stacked object laminae. These stepsare then repeated to successively build up the object lamina-by-lamina.This object formation technique may be generically called SelectiveDeposition Modeling (SDM). The main difference between this approach andthe first approach is that the material is deposited only in those areaswhich will become part of an object lamina. Typical of this approach isFused Deposition Modeling (FDM), as described in U.S. Pat. Nos.5,121,329 and 5,340,433, to Crump, in which the material is dispensed ina flowable state into an environment which is at a temperature below theflowable temperature of the material, and which then hardens after beingallowed to cool. A second example is the technology described in U.S.Pat. No. 5,260,009, to Penn. A third example is Ballistic ParticleManufacturing (BPM), as described in U.S. Pat. Nos. 4,665,492;5,134,569; and 5,216,616, to Masters, in which particles are directed tospecific locations to form object cross-sections. A fourth example isThermal Stereolithography (TSL) as described in U.S. Pat. No. 5,141,680,to Almquist et. Al.

When using SDM (as well as other RP&M building techniques), theappropriateness of various methods and apparatus for production ofuseful objects depends on a number of factors. As these factors cannottypically be optimized simultaneously, a selection of an appropriatebuilding technique and associated method and apparatus involve tradeoffs depending on specific needs and circumstances. Some factors to beconsidered may include 1) equipment cost, 2) operation cost, 3)production speed, 4) object accuracy, 5) object surface finish, 6)material properties of formed objects, 7) anticipated use of objects, 8)availability of secondary processes for obtaining different materialproperties, 9) ease of use and operator constraints, 10) required ordesired operation environment, 11) safety, and 12) post processing timeand effort.

In this regard there has been a long existing need to simultaneouslyoptimize as many of these parameters as possible to more effectivelybuild three-dimensional objects. As a first example, there has been aneed to enhance object production speed when building objects using thethird approach, SDM, as described above (e.g. Thermal Stereolithography)while simultaneously maintaining or reducing the equipment cost. As asecond example, there has been a long existing need for a low cost RP&Msystem useable in an office environment.

In SDM, as well as the other RP&M approaches, typically accurateformation and placement of working surfaces are required so that outwardfacing cross-sectional regions can be accurately formed and placed. Thefirst two approaches naturally supply working surfaces on whichsubsequent layers of material can be placed and lamina formed. However,since the third approach, SDM, does not necessarily supply a workingsurface, it suffers from a particularly acute problem of accuratelyforming and placing subsequent lamina which contain regions not fullysupported by previously dispensed material such as regions includingoutward facing surfaces of the object in the direction of the previouslydispensed material. In the typical building process where subsequentlaminae are placed above previously formed laminae this is particularlya problem for down-facing surfaces (down-facing portions of laminae) ofthe object. This can be understood by considering that the thirdapproach theoretically only deposits material in those areas of theworking surface which will become part of the corresponding objectlamina. Thus, nothing will be available to provide a working surface foror to support any down-facing surfaces appearing on a subsequentcross-section. Downward facing regions, as well as upward facing andcontinuing cross-sectional regions, as related to photo-basedStereolithography, but as applicable to other RP&M technologiesincluding SDM, are described in detail in U.S. Pat. Nos. 5,345,391, and5,321,622, to Hull et. al. and Snead et. al., respectively. The previouslamina is non-existent in down-facing regions and is thus unavailable toperform the desired support function. Similarly, unsolidified materialis not available to perform the support function since, by definition,in the third approach, such material is typically not deposited in areaswhich do not become part of an object cross-section. The problemresulting from this situation may be referred to as the “lack of workingsurface” problem.

The “lack of working surface” problem is illustrated in FIG. 1, whichdepicts two laminae, identified with numerals 1 and 2, built using athree-dimensional modeling method and apparatus. As shown, lamina 1,which is situated on top of lamina 2, has two down-facing surfaces,which are shown with cross-hatch and identified with numerals 3 and 4.Employing the SDM approach described above, unsolidified material isnever deposited in the volumes directly below the down-facing surfaces,which are identified with numerals 5 and 6. Thus, with the SDM approach,there is nothing to provide a working surface for or to support the twodown-facing surfaces.

Several mechanisms have been proposed to address this problem, butheretofore, none has proven completely satisfactory. One such mechanism,suggested or described in U.S. Pat. No. 4,247,508, to Housholder; U.S.Pat. Nos. 4,961,154; 5,031,120; 5,263,130; and 5,386,500, to Pomerantz,et al.; U.S. Pat. No. 5,136,515, to Helinski; U.S. Pat. No. 5,141,680,to Almquist, et al.; U.S. Pat. No. 5,260,009, to Penn; U.S. Pat. No.5,287,435, to Cohen, et al.; U.S. Pat. No. 5,362,427, to Mitchell; U.S.Pat. No. 5,398,193, to dunghills; U.S. Pat. Nos. 5,286,573 and5,301,415, to Prinz, et al., involves filling the volumes belowdown-facing surfaces with a support material different from that used tobuild the object, and presumably easily separable from it (by means ofhaving a lower melting point, for example). In relation to FIG. 1, forexample, the volumes identified with numerals 5 and 6 would be filledwith the support material prior to the time that the material used toform down-facing surfaces 3 and 4 is deposited.

A problem with the two material (i.e. building material and differentsupport material) approach is that it is expensive and cumbersomebecause of the inefficiencies, heat dissipation requirements, and costsassociated with handling and delivering the support, or second,material. For example, a separate material handling and dispensingmechanism for the support material may have to be provided.Alternatively, means may have to be provided to coordinate the handlingand delivery of both materials through a single system.

Another approach, described in U.S. Pat. No. 4,999,143, to Hull, et al.;U.S. Pat. No. 5,216,616, to Masters; and U.S. Pat. No. 5,386,500, toPomerantz, et al., is to build generally spaced support structures fromthe same material as that used to build the object. A multitude ofproblems have occurred with this approach. A first problem has involvedthe inability to make support structures of arbitrary height whilesimultaneously ensuring that they were easily separately from theobject. Second, a problem has been encountered regarding the inabilityto achieve easy separability between object and support structure whilesimultaneously maintaining an effective working surface for the buildingof and support of the outward facing surfaces. A third problem involvesthe inability to accumulate support structure in the directionperpendicular to the planes of the cross-sections (e.g. verticaldirection) at approximately the same rate as that at which the objectaccumulates. A fourth problem has involved the inability to ensure easyseparability and minimal damage to up-facing surfaces when supports mustbe placed thereon in order to support down-facing surfaces thereabovewhich are part of subsequent layers. A fifth issue has involved thedesire to increase system throughput.

To illustrate, the objective of achieving easy separability dictatesthat the surface area over which each support contacts the object bekept as small as possible. On the other hand, the objective ofaccumulating a support in the Z-direction at a rate approximating thatof object accumulation dictates that the cross-sectional area of eachsupport be as large as possible to provide a large area to perimeterratio thereby minimizing loss of material for build up in theZ-direction due to run off, spreading, mis-targeting and the like byallowing a large target area to compensate for any inaccuracies in thedeposition process and to limit the ability of material to spreadhorizontally instead of building up vertically.

Further, the objective of achieving minimal damage to the down-facingsurface dictates that the spacing between the supports be kept as largeas possible in order to minimize the area of contact between thesupports and the object. On the other hand, the objective of providingan effective working surface for the building of the down-facing surfacedictates that the spacing be kept as small as possible. As is apparent,there is a conflict in simultaneously achieving these objectives.

This problem is illustrated in FIG. 2, in which, compared to FIG. 1,like elements are referenced with like numerals. As shown, down-facingsurface 3 is supported through columnar supports 7a, 7b, and 7c, whiledown-facing surface 4 is supported through columnar supports 8a, 8b, 8c,and 8d. Columnar supports 7a, 7b, and 7c are widely spaced from oneanother in order to minimize damage to down-facing surface 3. Moreover,they are each configured to contact the down-facing surface over arelatively small surface area to enhance separability. On the otherhand, because of their small cross-sectional surface area, they may notbe able to accumulate, in the vertical direction, fast enough to keep upwith the rate of growth of the object. Moreover, because of their widespacing, they may not be able to provide an effective working surfacefor the building of and support of down-facing surface 3.

Columnar supports 8a, 8b, 8c, and 8d, by contrast, are more closelyspaced together in order to provide a more effective working surface forthe building and support of down-facing surface 4. Also, each isconfigured with a larger surface area to enable them to grow at rateapproximating that of the object. Unfortunately, because of their closerspacing and larger cross-sectional area, these supports will cause moredamage to the down-facing surface when they are removed.

All patents referred to herein above in this section of thespecification are hereby incorporated by reference as if set forth infull.

3. Attached Appendices and Related Patents and Applications

Appendix A is attached hereto and provides details of prefered ThermalStereolithography materials for use in the some preferred embodiments ofthe invention.

The following applications are hereby incorporated herein by referenceas if set forth in full herein:

Application Title Filing Date No. Status 9/27/95 08/535,772 SelectiveDeposition Abandoned Modeling Materials and Method 9/27/95 08/534,477Selective Deposition Abandoned Modeling Method and System

The assignee of the subject application, 3D Systems, Inc., is filingthis application concurrently with the following related application,which is incorporated by reference herein as though set forth in full:

Application Docket No. Filing Date No. Title Status 08/722,326 9/27/9608/722,326 Method and Apparatus for 5,943,235 Data Manipulation andSystem Control in a Selective Deposition Modeling System

According to Thermal Stereolithography and some Fused DepositionModeling techniques, a three-dimensional object is built up layer bylayer from a material which is heated until it is flowable, and which isthen dispensed with a dispenser. The material may be dispensed as asemi-continuous flow of material from the dispenser or it mayalternatively be dispensed as individual droplets. In the case where thematerial is dispensed as a semi-continuous flow, it is conceivable thatless stringent working surface criteria may be acceptable. An earlyembodiment of Thermal Stereolithography is described in U.S. Pat.No.5,141,680. Thermal Stereolithography is particularly suitable for usein an office environment because of its ability to use non-reactive,non-toxic materials. Moreover, the process of forming objects usingthese materials need not involve the use of radiations (e.g. UVradiation, IR radiation, visible light and/or other forms of laserradiation), heating materials to combustible temperatures (e.g. burningthe material along cross-section boundaries as in some LOM techniques),reactive chemicals (e.g. monomers, photopolymers) or toxic chemicals(e.g. solvents), complicated cutting machinery, and the like, which canbe noisy or pose a significant risks if mishandled. Instead, objectformation is achieved by heating the material to a flowable temperaturethen selectively dispensing the material and allowing it to cool.

U.S. patent application Ser. No. 08/534,447, now abandoned, referencedabove, is directed to data transformation techniques for use inconverting 3D object data into support and object data for use in apreferred Selective Deposition Modeling (SDM) system based on SDM/TSLprinciples. This referenced application is also directed to various datahandling, data control, and system control techniques for controllingthe preferred SDM/TSL system described hereinafter. Some alternativedata manipulation techniques and control techniques are also describedfor use in SDM systems as well as for use in other RP&M systems.

U.S. patent application Ser. No. 08/535,772, now abandoned, asreferenced above, is directed to the preferred material used by thepreferred SDM/TSL system described herein. Some alternative materialsand methods are also described.

U.S. patent application Ser. No. 08/534,477, now abandoned, asreferenced above, is directed to some particulars of the preferredSDM/TSL system. Some alternative configurations are also addressed.

The assignee of the instant application, 3D Systems, Inc., is also theowner of a number of other U.S. patent applications and U.S. patents inRP&M field and particularly in the photo-based Stereolithography portionof that field. These patents include disclosures which can be combinedwith the teachings of the instant application to provide enhanced SDMobject formation techniques. The following commonly owned U.S. patentapplications and U.S. patents are hereby incorporated by reference as ifset forth in full herein:

App No. Status and/or Filing Date Topic Patent No. 08/484,582Fundamental elements of Stereolithography are taught. 5,573,722 Jun 7,1995 08/475,715 Various recoating techniques for use in SL are 5,667,820Jun 7, 1995 described including a material dispenser that allows forselective deposition from a plurality of orifices. 08/479,875 VariousLOM type building techniques are described. 5,637,169 Jun 7, 199508/486,098 A description of curl distortion is provided along withAbandoned Jun 7, 1995 various techniques for reducing this distortion.08/475,730 A description of a 3D data slicing technique for 5,854,748Jun 7, 1995 obtaining cross-sectional data is described which utilizesBoolean layer comparisons to define down- facing, up-facing andcontinuing regions. Techniques for performing cure-width compensationand for producing various object configurations relative to an initialCAD design are also described. 08/480,670 A description of an early SLSlicing technique is 5,870,307 Jun 7, 1995 described including vectorgeneration and cure width compensation. 08/428,950 Various buildingtechniques for use in SL are described Abandoned Apr 25, 1995 includingvarious build styles involving alternate sequencing, vector interlacingand vector offsetting for forming semi-solid and solid objects.08/428,951 Simultaneously Multiple Layer Curing techniques for 5,999,184Apr 25, 1995 SL are taught including techniques for performing verticalcomparisons, correcting errors due to over curing in the z-direction,techniques for performing horizontal comparisons, and horizontal erosionroutines. 08/405,812 SL recoating techniques using vibrational energyare 5,688,464 Mar 16, 1995 described. 08/402,553 SL recoating techniquesusing a doctor blade and liquid 5,651,934 Mar 13, 1995 level controltechniques are described. 08/382,268 Several SL recoating techniques aredescribed Abandoned Feb 1, 1995 including techniques involving the useof ink jets to selectively dispense material for forming a next layer ofunsolidified material. 08/148,544 Fundamental elements of thermalstereolithography are 5,501,824 Nov 8, 1993 described. 07/182,801Support structures for SL are described. 4,999,143 Apr 18, 198807/183,015 Placement of hole in objects for reducing stress are5,015,424 Apr 18, 1988 described. 07/365,444 Integrated SL building,cleaning and post curing 5,143,663 Jun 12, 1989 techniques aredescribed. 07/824,819 Various aspects of a large SL apparatus aredescribed. 5,182,715 Jan 22, 1992 07/605,979 Techniques for enhancingsurface finish of SL objects 5,209,878 Oct 30, 1990 are describedincluding the use of thin fill layers in combination with thickerstructural layers and meniscus smoothing. 07/929,463 Powder coatingtechniques are described for enhancing 5,234,636 Aug 13, 1991 surfacefinish. 07/939,549 Building techniques for reducing curl distortion inSL 5,238,639 Aug 31, 1992 (by balancing regions of stress and shrinkage)are described.

SUMMARY OF THE INVENTION

The instant invention embodies a number of techniques (methods andapparatus) that can be used alone or in combination to address a numberof problems associated with building and supporting objects formed usingSelective Deposition Modeling techniques. Though primarily directed toSDM techniques, the techniques described hereinafter can be applied in avariety of ways (as will be apparent to one of skill in the art whoreads the instant disclosure) to the other RP&M technologies asdescribed above to enhance object accuracy, surface finish, build timeand/or post processing effort and time. Furthermore, the techniquesdescribed herein can be applied to Selective Deposition Modeling systemsthat use one or more building and/or support materials wherein one ormore are selectively dispensed and in which others may be dispensednon-selectively and wherein elevated temperatures may or may not be usedfor all or part of the materials to aid in their deposition.

The techniques can be applied to SDM systems wherein the buildingmaterial (e.g. paint or ink) is made flowable for dispensing purposes byadding a solvent (e.g. water, alcohol, acetone, paint thinner, or othersolvents appropriate for specific building, wherein the material issolidifiable after or during dispensing by causing the removal of thesolvent (e.g. by heating the dispensed material, by dispensing thematerial into a partially evacuated (i.e. vacuumed) building chamber, orby simply allowing sufficient time for the solvent to evaporate).Alternatively, or additionally, the building material (e.g. paint) maybe thixotropic in nature wherein an increase in shear force on thematerial could be used to aid in its dispensing or the thixotropicproperty may simply be used to aid the material in holding its shapeafter being dispensed. Alternatively, and/or additionally, the materialmay be reactive in nature (e.g. a photopolymer, thermal polymer, one ortwo-part epoxy material, a combination material such as one of thementioned materials in combination with a wax or thermal plasticmaterial) or at least solidifiable when combined with another material(e.g. plaster of paris & water), wherein after dispensing, the materialis reacted by appropriate application of prescribed stimulation (e.g.heat, EM radiation [visible, IR, UV, x-rays, etc.], a reactive chemical,the second part of a two part epoxy, the second or multiple part of acombination) such that the building material and/or combination ofmaterials become solidified. Of course, Thermal Stereolithographicmaterials and dispensing techniques may be used alone or in combinationwith the above alternatives. Furthermore, various dispensing techniquesmay be used such as dispensing by single or multiple ink jet devicesincluding, but not limited to, hot melt ink jets, bubble jets, etc., andcontinuous or semi-continuous flow, single or multiple orifice extrusionnozzles or heads.

Accordingly it is a first object of the invention to provide a methodand apparatus for higher accuracy production of objects.

A second object of the invention is to provide a method and apparatusfor production of objects with less distortion by controlling thethermal environment during object formation.

A third object of the invention is to provide a method and apparatus forproduction of objects with less distortion by controlling how materialis dispensed.

A fourth object of the invention is to provide a method and apparatusfor enhancing object production speed.

A fifth object of the invention is to provide a support structure methodand apparatus that allows object supports of arbitrary height to beformed.

A sixth object of the invention is to provide a support structure methodand apparatus that provides a good working surface.

A seventh object of the invention is to provide a method and apparatusthat forms a support structure that is easily removed from down-facingsurfaces of the object.

An eighth object of the invention is to provide a support structuremethod and apparatus that results in minimum damage to down-facingsurfaces of the object upon removal thereof.

A ninth object of the invention is to provide a method and apparatus forremoving the supports from the object.

A tenth object of the invention is to provide a support structure methodand apparatus that builds up supports vertically at a rate approximatingthe vertical build up rate of the object.

An eleventh object of the invention is to provide a method and apparatusthat forms a support structure that is easily removed from up-facingsurfaces of the object.

A twelfth object of the invention is to provide a support structuremethod and apparatus that results in minimum damage to up-facingsurfaces of the object upon removal thereof.

A thirteenth object of the invention is to provide a method andapparatus for producing supports that are separated from vertical objectsurfaces.

A fourteenth object is to provide support structures that are combinablewith other RP&M technologies for enhanced object formation.

It is intended that the above objects can be achieved separately bydifferent aspects of the invention and that additional objects of theinvention will involve various combinations of the above independentobjects such that combined benefits may be obtained from combinedtechniques.

Other objects of the invention will be apparent from the descriptionherein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates down-facing surfaces of an object;

FIG. 2 illustrates two categories of support structures for supportingthe down-facing surfaces of FIG. 1;

FIG. 3 is a diagram of the main functional components of the preferredSelective Deposition Modeling/Thermal Stereolithography system;

FIGS. 4a and 4 b illustrate the orifice plate of the print head of FIG.3 at different orientations to the scanning direction;

FIG. 5 is a more detailed drawing of the planarizer of FIG. 3;

FIG. 6 illustrates the relative spacing between adjacent nozzles on theorifice plate and adjacent raster lines;

FIG. 7 illustrates the grid of pixels which defines the data resolutionof the system;

FIG. 8 illustrates two perpendicular examples of raster lineorientation;

FIG. 9 illustrates two examples of deposition propagation in thesecondary scanning direction;

FIGS. 10a and 10 b illustrate two examples of deposition propagation inthe main scanning direction;

FIGS. 11a and 11 b illustrate an example of scan line interlacing;

FIGS. 12a and 12 b illustrate an example of drop location interlacingalong several scan lines;

FIGS. 13a and 13 b illustrate a further example of drop locationinterlacing along several scan lines;

FIG. 14 illustrates a single pixel checkerboard deposition pattern;

FIG. 15 illustrates a 3×3 column support pixel pattern forming apreferred support structure;

FIGS. 16a-16 d illustrates several overprinting schemes;

FIGS. 17a and 17 b illustrates a mis-registration problem that can occurwhen using an overprinting technique;

FIG. 18 illustrates the resulting deposition regions when the pixels ofFIG. 15 are exposed using an overprinting scheme;

FIG. 19 illustrates an alternative pixel pattern for column supports;

FIG. 20 illustrates a Hybrid support structure;

FIGS. 21a and 21 b illustrate arch-type supports;

FIGS. 22a-d depict an interlacing embodiment for depositing materialduring the building of an object;

FIGS. 23a-h illustrate a building embodiment which uses horizontal andvertical pixel offsets;

FIGS. 24a-d illustrate a deposition embodiment that reduces risk ofbridging between regions separated by a gap;

FIGS. 25a-e illustrate a building technique wherein the object isseparated into pieces, built separately and then adhered together;

FIG. 26 illustrates a preferred two step raster scanning and indexingpattern;

FIGS. 27a- 27 e depict various combinations of working surface andtargeting positions;

FIG. 28a depicts a side view of an embodiment of branching supports;

FIG. 28b depicts a side view of another embodiment of branchingsupports;

FIGS. 29a- 29 e depict a top view of branching layers for an embodimentof branching supports;

FIGS. 30a- 30 m depict a top view of branching layers for anotherembodiment of branching supports;

FIGS. 31a-31 c depict a top view of branching layers for anotherembodiment of branching supports; and

FIGS. 32a- 31 d depict a top view of branching layers for anotherembodiment of branching supports.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

As previously discussed, the subject application is directed to supporttechniques and building techniques appropriate for use in a SelectiveDeposition Modeling (SDM) system. In particular, the preferred SDMsystem is a Thermal Stereolithography (TSL) system. The Description OfThe Preferred Embodiments will begin with a description of the preferredTSL system. A more detailed description of the preferred system, datamanipulation techniques, system control techniques, materialformulations and properties, and various alternatives are described inpreviously referenced and incorporated U.S. patent application Ser. Nos.08/534,813; 08/534,447, now abandoned; 08/535,772; and 08/534,477, nowabandoned; and U.S. Pat. No. 5,943,235, filed concurrently herewith.Further, alternative systems are discussed in a number of the previouslyincorporated applications and patents, especially those referenced asbeing directly related to, or applicable to, SDM, TSL or FusedDeposition Modeling (FDM). As such, the support structures and buildstyles described hereinafter should be construed as applicable to avariety of SDM, TSL and FDM systems and not limited by the systemexamples described herein. Furthermore, as noted previously, thesesupport structures and build styles have utility in the other RP&Mtechnologies.

A preferred embodiment of an apparatus for performing SDM/TSL isillustrated in FIG. 3. The apparatus comprises a dispensing platform 18,a dispensing head 9 (e.g. multi orifice ink jet head), wherein thedispensing head 9 is located on the dispensing platform 18, a planarizer11 and a part-building platform, 15. The dispensing platform 18 is ahorizontal member which is capable of supporting the planarizer 11 andthe dispensing head 9. The dispensing platform 18 is slidably coupled toan X-stage 12 through a coupling member 13. The X-stage 12 is preferablycontrolled by a control computer or microprocessor (not shown) andcontrollably moves the dispensing platform 18 back and forth in theX-direction, or the main scanning direction.

Furthermore, at either side of the platform 18, fans (not shown) aremounted for blowing air vertically downward to help cool the dispensedmaterial 14 and part-building platform 15 such that the desired buildingtemperature is maintained. Other suitable mounting schemes for the fansand/or other cooling systems include, but are not limited to, mistingdevices for directing vaporizable liquids (e.g. water, alcohol, orsolvents) onto the surface of the object, forced air cooling deviceswith fans mounted between the planarizer 11 and the dispensing head 9,and forced air cooling devices with stationary or moving fans mountedoff the dispensing platform. Cooling systems may include active orpassive techniques for removing heat which may be computer controlled incombination with temperature sensing devices to maintain the previouslydispensed material within the desired building temperature range. Otherapproaches to cooling include, but are not limited to, salting thematerial with a substance which functions as a black body radiator,especially at IR frequencies, such that heat is more readily radiatedfrom the object during the building process. Further alternativeapproaches include, but are not limited to, adding a conductivesubstance to the material every few layers, adding a solvent to thematerial, building parts with cooling passages or with an embeddedsubstrate (such as interlaced wires) for cooling, or building on a glassplate or Mylar® sheet.

Other embodiments for cooling the material or at least maintaining thedispensed material at an appropriate temperature, might involve the useof directing a temperature moderating gas (e.g. a cooling gas such asair) at the upper surface of the partially formed object, as discussedabove, but they may additionally include controlled techniques forremoving the cooling air from the surface. Such techniques might involvethe use of blowing and sucking devices and alternate positioning ofblowing ducts (gas inserting ducts) and sucking ducts (gas removingducts). These ducts may allow the cooling gas to be removed beforeexcessive heating of the gas causes a loss in effective cooling rate.The gas directed at the surface may be introduced in a cooled state,introduced at room temperature, or introduced at some other appropriatetemperature. If appropriately configured, these alternate inserting andremoving ducts may allow faster scanning speed than presently allowabledue to turbulence or wind distortion of fragile structures such assupports. These ducts might be configured to provide air flow in theopposite direction to print head movement thereby reducing the net windvelocity coming into contact with the partially formed object. Theblowing or sucking associated with individual ducts may be reversed,turned on, or turned off depending on the direction of movement of theprint head.

The print head 9 is a commercial print head configured for jetting hotmelt inks such as, for example, thermal plastics or wax-like materials,and modified for use in a three-dimensional modeling system, wherein theprint head undergoes back and forth movements and accelerations. Theprint head modifications include configuring any on board reservoir suchthat the accelerations result in minimal misplacement of material in thereservoir. One preferred embodiment includes a 96 jet commercial printhead, Model No. HDS 96i, sold by Spectra Corporation, Nashua, N.H.including reservoir modifications. The print head is supplied materialin a flowable state from a Material Packaging & Handling Subsystem (notshown), which is described in the previously referenced U.S. patentapplication Ser. No. 08/534,477, now abandoned. In the preferredembodiment, all 96 jets on the head are computer controlled toselectively fire droplets through orifice plate 10 when each orifice(i.e. jet) is appropriately located to dispense droplets onto desiredlocations. In practice, approximately 12,000 to 16,000 commands persecond have been sent to each jet selectively commanding each one tofire (dispense a droplet) or not to fire (not to dispense a droplet)depending on jet position and desired locations for material deposition.Also, in practice, firing commands have been sent simultaneously to alljets. Since, the preferred print head mentioned above contains almost100 jets, the above noted firing rates result in the need to sendapproximately 1.2 to 1.6 million firing commands to the head eachsecond. Thus, the head is computer controlled so as to selectively firethe jets and cause them to simultaneously emit droplets of the moltenmaterial through one or more orifices in orifice plate 10. Of course, itwill be appreciated that in alternative preferred embodiments, headswith different numbers of jets can be used, different firing frequenciesare possible, and in appropriate circumstances non-simultaneous firingof the jets is possible.

To most effectively build a three-dimensional object, it is desired thatall of the jets fire correctly. To ensure that all jets are firingcorrectly or at least maximize the number which are firing correctly,various techniques can be used. One such embodiment involves checkingthe jets after formation of each lamina. This technique includes thesteps of: 1) forming a lamina; 2) checking the jets by printing a testpattern of lines on a piece of paper, with all jets firing; 3) opticallydetecting (through bar code scanning or the like) whether a jet ismisfiring; 4) unclogging the jet; 5) removing the entirety of thejust-dispensed layer (e.g. by machining using a preferred planarizer tobe described herein after); and 6) rebuilding the layer with all jetsincluding the unclogged jet.

A second embodiment involves the following preferred steps: 1) forming alayer; 2) optically detecting a misfiring jet; 3) rescanning the lineson the layer that should have been formed by the misfiring jet; 4)ceasing the use of the misfiring jet in the remainder of the buildingprocess; and 5) scanning subsequent layers while compensating for themisfiring jet (i.e., make extra passes with a working jet to cover thelines corresponding to the misfiring jet). Optionally, the misfiring jetmay be periodically checked to see if it has started functioning again.If so, this jet is put back into operation. Another option involvesputting a misfiring jet through a reactivation routine to see if it canbe made operational. This could occur during the building process orduring servicing of the system. As a further alternative, it may bepossible to determine whether or not a jet is firing correctly bytracking the electrical characteristics of the piezo electric element asfiring is to occur.

A third embodiment might involve the use of a flexible element forwiping excess material from the bottom of the print head. Thisembodiment involves the firing of all the jets followed by a wiping ofthe orifice plate with a heated rubber (e.g. VITON) blade. Preferablythe blade is positioned such that it contacts the orifice plate as theyare relatively moved passed each other thereby causing a squeegee actionto remove excess material from the orifice plate and hopefullyrevitalizing any jets which were not behaving properly. It is furtherpreferred that the orifice plate and blade be positioned at an angle toeach other such that at any one time during their contact only a portionof the orifice plate is in contact with the squeegee thereby minimizingthe force the blade exerts on the orifice plate.

The orifice plate 10 is mounted on the dispensing platform 18 such thatdroplets of material are allowed to emit from the underside of thedispensing platform 18. The orifice plate 10 is illustrated in FIGS. 4aand 4 b. In one preferred embodiment, and as depicted in FIG. 4a, theorifice plate 10 (i.e. the line of orifices) is mounted approximatelyperpendicular to the main scanning direction (X-direction) and isconfigured with N=96 individually controllable orifices (labeled 10(1),10(2), 10(3) . . . 10(96)). Each orifice is equipped with apiezoelectric element that causes a pressure wave to propagate throughthe material when an electric firing pulse is applied to the element.The pressure wave causes a drop of material to be emitted from theorifice. The 96 orifices are controlled by the control computer whichcontrols the rate and timing of the firing pulses applied to theindividual orifices. With reference to FIG. 4a, the distance “d” betweenadjacent orifices in the preferred embodiment is about {fraction(8/300)} of an inch (about 26.67 mils or 0.677 mm). Thus, with 96orifices, the effective length “D” of the orifice plate is about(N×{fraction (8/300 )} inch)=(96×{fraction (8/300)} inches)=2.56 inches(65.02 mm).

To accurately build an object, the print head must fire such that thedroplets reach particular “desired drop locations”, i.e., locations thatthe droplet is intended to land. The desired drop locations aredetermined from a data map, or pixel locations, which describes theobject as a series of relatively spaced location points. For thedroplets to land at the desired drop locations, the print head must firethe droplets from a “desired firing location” or at a “desired firingtime” which is based on the relative position of the print head to thedesired drop location, the velocity of the print head, and the ballisticcharacteristics of the particles after being ejected.

In a preferred embodiment raster scanning is used to position the printhead 9 and orifices at desired firing locations. The printing processfor each lamina is accomplished by a series of relative movementsbetween the head 9 and the desired drop or firing locations. Printingtypically occurs as the head 9 relatively moves in a main scanningdirection. This is followed by a typically smaller increment of movementin a secondary scanning direction while no dispensing occurs, which inturn is followed by a reverse scan in the main scanning direction inwhich dispensing again occurs. The process of alternating main scans andsecondary scans occurs repeatedly until the lamina is completelydeposited.

Alternative preferred embodiments may perform small secondary scanningmovements while main scanning occurs. Because of the typically largedifference in net scanning speed along the main and secondary directionssuch an alternative still results in deposition along scanning lineswhich are nearly parallel to the main scanning direction andperpendicular to the secondary scanning direction. Further alternativepreferred embodiments may utilize vector scanning techniques or acombination of vector scanning and raster scanning techniques.

It has been found that droplets, immediately after being dispensed fromthe jet orifice, have an elongated shape, compared to their width. Theratio of droplet length to width can be defined as the aspect ratio ofthe droplet. It has further been found that the aspect ratio of thesedroplets becomes smaller as the droplets travel away from the jetorifice (i.e. they become more spherical in shape).

It should be appreciated that in some embodiments the spacing betweenthe orifice plate 10 and the working surface is preferably large enoughsuch that the drops emitted therefrom have become semi-circular in shapewhen they impact the working surface. On the other hand, it should alsobe appreciated that this spacing, which determines the distance thedroplets must travel during the printing process before impact, shouldbe minimized in order to avoid accuracy problems which may occur as thetravel time is increased. In practice, it has been found that these twoconditions are both satisfactorily met when at least 90% of the dropletsemitted from the orifice plate have achieved an aspect ratio (i.e., theratio formed by the width of the droplet divided by its length) which ispreferably less than about 1.3, more preferably less than about 1.2, andmost preferably, which is between about 1.05 and 1.1.

In alternative preferred embodiments, the print head 9 may be mounted ata non-perpendicular angle to the main scanning direction. This situationis depicted in FIG. 4b wherein the print head 9 is mounted at an angle“α” to the main scanning direction (e.g., the “X” direction). In thisalternative situation the separation between the orifices is reducedfrom d to d′=(d×sin α) and the effective length of the print head 9 isreduced to D′=(D×sin α). When the spacing d′ is equal to the desiredprint resolution in the secondary scanning direction (directionapproximately perpendicular to the main scanning direction), the angle αis considered to be the “saber angle”.

If the spacing d or d′ is not at the desired secondary print resolution(i.e. the print head is not at the saber angle) then for optimalefficiency in printing a layer, the desired resolution must be selectedsuch as to make d or d′ an integer multiple of the desired resolution.Similarly, when printing with α≠90°, a spacing between jets exists inthe main scanning direction as well as the secondary scanning direction.This spacing is defined by d″=d×cos α. This in turn dictates thatoptimization of printing efficiency will occur when the desired maindirection print resolution is selected to be an integral divisor of d″(this assumes that firing locations are located in a rectangular grid).Another way of expressing this is that the angle α is selected such thatd′ and/or d″ when divided by appropriate integers M and P yield thedesired secondary and main scanning resolutions. An advantage to usingthe preferred print head orientation (α=90°) is that it allows anydesired printing resolution in the main scanning direction while stillmaintaining optimal efficiency.

In other preferred embodiments, multiple heads may be used which lay endto end (extend in the secondary scanning direction) and/or which arestacked back to back (stacked in the main scanning direction). Whenstacked back to back, the print heads may have orifices aligned in themain scanning direction so that they print over the same lines oralternatively they may be offset from one another so as to dispensematerial along different main scanning lines. In particular, it may bedesirable to have the back to back print heads offset from each other inthe secondary scanning direction by the desired raster line spacing tominimize the number of main scanning passes that must occur. In otherpreferred embodiments, the data defining deposition locations may not belocated by pixels configured in a rectangular grid but instead may belocated by pixels configured in some other pattern (e.g. offset orstaggered pattern). More particularly, the deposition locations may befully or partially varied from layer to layer in order to performpartial pixel drop location offsetting for an entire layer or for aportion of a layer based on the particulars of a region to be jetted.

Presently preferred printing techniques involve deposition resolutionsof 300, 600 and 1200 drops per inch in the main scanning direction and300 drops per inch in the secondary scanning direction.

With reference to FIGS. 3 and 5, the planarizer 11 includes a heatedrotating (e.g. 2000 rpm) cylinder 18 a with a textured (e.g. knurled)surface. Its function is to melt, transfer and remove portions of thepreviously dispensed layer or lamina of material in order to smooth itout, to set a desired thickness for the last formed layer, and to setthe net upper surface of the last formed layer to a desired level.Numeral 19 identifies a layer of material which was just deposited bythe print head. The rotating cylinder 18 a is mounted in the dispensingplatform such that it is allowed to project from the underside of theplatform by a sufficient amount in the Z-direction such that it contactsmaterial 19 at a desired level. More importantly the rotating cylinder18 a is mounted so as to project a desired distance below the planeswept out by the underside of the print head or orifice plate. In theevent that the orifice plate itself projects below the dispensingplatform 18, the rotating cylinder 18 a will project further below thedispensing platform 18. In one preferred embodiment, the projectionbelow the orifice plate in the z-direction is in the range of 0.5 mm to1.0 mm. The extent to which the roller extends below the dispensingplatform 18 is a determinant of the spacing between the orifice plate 10and the working surface. Thus, in some preferred embodiments it ispreferred that the extent to which the planarizer 11 extends below theorifice plate 10 not conflict with the condition described earlier inrelation to droplet aspect ratio, in which 90% of the droplets haveachieved an aspect ratio upon impact preferably less than about 1.3,more preferably less than about 1.2, and most preferably between about1.05-1.1.

The rotation of the cylinder sweeps material from the just-depositedlayer, identified in the figure with numeral 21, leaving in its wakesmooth surface 20. The material 21 adheres to the knurled surface of thecylinder and is displaced until it contacts wiper 22. As shown, wiper 22is disposed to effectively “scrape” the material 21 from the surface ofthe cylinder. The wiper is preferably made of VITON, although othermaterials, such as TEFLON®, are capable of scraping the material fromthe surface of the cylinder are also suitable. Preferably the scrappermaterial is non-wetting with respect to the liquefied building materialand is durable enough to contact the rotating cylinder 18 a withoutwearing out too quickly. The removed material is drawn away undersuction via a heated umbilical to a waste tank (not shown), where it iseither disposed of or recycled. The planarizer waste tank is heldconstantly under vacuum in order to continuously remove material fromthe planarizer cylinder. When the tank becomes full the systemautomatically reverses the vacuum for a few seconds to purge the wastematerial out of a check valve into a larger waste tray. Once empty,vacuum is restored and waste continues to be drawn from the planarizer.In practice, it has been observed that approximately 10-15% of thematerial dispensed is removed by the planarizer. Though most preferredembodiments use a combination of rotating, melting and scraping toperform planarization, it is believed that other embodiments mightutilize any one of these three elements or any combination of two ofthem.

In present implementations, the cylinder 18 a rotates (e.g. atapproximately 2000 rpm) in a single direction as the head moves back inforth in each direction. In alternative embodiments, the cylinder 18 acan be made to rotate in opposite directions based on the forward orreverse direction that platform 18 sweeps while moving in the mainscanning direction. Some embodiments might involve the axis of rotationof cylinder 18 a being off axis relative to the axis of orientation ofthe print head. In other embodiments more than one cylinder 18 a may beused. For example, if two cylinders were used, each one may be caused torotate in different directions and may further be verticallypositionable so as to allow a selected one to participate inplanarization during any given sweep.

When using a single print head 10 and cylinder 18 a, planarization onlyeffectively occurs on every second pass of the print head thoughdeposition occurs on each pass (i.e. planarization always occurs in thesame direction). Under these conditions, planarization occurs when thesweeping direction points along the same direction as an arrow pointingfrom the cylinder to the print head. In other words planarization occurswhen the sweeping direction is such that the cylinder follows the printhead as the elements traverse the layer in the main scanning direction.

Other preferred embodiments might use a single cylinder, but use one ormore print heads located on either side of the cylinder, such thatplanarization effectively occurs when sweeping in both directions. Otheralternative embodiments might decouple the movement of the print head(s)and the planarizing cylinder. This decoupling might allow independentplanarization and dispensing activity. Such decoupling might involve thedirections of print head sweeping (e.g. X-direction) and cylindersweeping (e.g. Y-direction) being different. Such decoupling might alsoallow multiple layers to be formed or lines of a single layer to bedeposited between planarization steps.

With reference to FIG. 3, part-building platform 15 is also provided.The three-dimensional object or part, identified in the figure withreference numeral 14, is built on the platform 15. The platform 15 isslidably coupled to Y-stage 16 a and 16 b which controllably moves theplatform back and forth in the Y-direction (i.e., index direction orsecondary scanning direction) under computer control. The platform 15 isalso coupled to Z-stage 17 which controllably moves the platform up anddown (typically progressively downward during the build process) in theZ-direction under computer control.

To build a cross-section, lamina, or layer of a part, the Z-stage isdirected to move the part-building platform 15 relative to the printhead 9 such that the last-built cross-section of the part 14 is situatedan appropriate amount below the orifice plate 10 of the print head 9.The print head 9 in combination with the Y-stage 16 a, 16 b is thencaused to sweep one or more times over the XY build region (the headsweeps back and forth in the X direction, while the Y-stage 16 a, 16 btranslates the partially formed object in the Y-direction). Thecombination of the last formed cross-section, lamina, or layer of theobject and any supports associated therewith define the working surfacefor deposition of the next lamina and any supports associated therewith.During translation in the XY directions, the jet orifices of the printhead 9 are fired in a registered manner with respect to previouslydispensed layers to deposit material in a desired pattern and sequencefor the building of the next lamina of the object. During the dispensingprocess a portion of the dispensed material is removed by the planarizer11 in the manner discussed above. The X, Y and Z movements, dispensing,and planarizing are repeated to build up the object from a plurality ofselectively dispensed and adhered layers. Moreover, platform 15 can beindexed in either the Y- or Z- direction while the direction of thedispensing platform 18 is in the process of being reversed upon thecompletion of a scan.

In a preferred embodiment, the material deposited during the formationof a lamina has a thickness at or somewhat greater than the desiredlayer thickness. As described above the excess material deposited isremoved by the action of the planarizer. Under these conditions, theactual build up thickness between layers is not determined by the amountof material deposited for each layer but instead is determined by thedown-ward vertical increment made by the platform after deposition ofeach layer. If one wants to optimize build speed and/or minimize theamount of material wasted, it is desirable to trim off as littlematerial as possible during the deposition process. The less materialtrimmed off, the thicker each lamina is and the faster the object buildsup. On the other hand if one makes the layer thickness, i.e.z-increment, too large then the amount of build up associated with atleast some drop locations will begin to lag behind the desired level.This lag will results in the actual physical working surface being at adifferent position from the desired working surface and probably resultsin the formation of a non-planar working surface. This difference inposition can result in the XY misplacement of droplets due to a longertime of flight for than expected and it can further result in thevertical misplacement of object features that happen to begin or end atthe layers in which the actual working surface is mis-positioned.Therefor in some embodiments it is desirable to optimize layerincrementing in the vertical direction.

To determine an optimum Z-axis increment, an accumulation diagnosticpart may be used. This technique preferably involves building layers ofone or more test parts at successively greater Z-increments, measuringthe height of the features formed and determining which Z-incrementsgave rise to formation heights (i.e. vertical accumulation) of thecorrect amount and which Z-increments gave rise to formation heightswhich lagged behind the desired amount. It is expected thatlayer-increments (i.e. Z-increments) up to a certain amount (i.e. themaximum acceptable amount) would yield build up levels for the objectequal to that predicted by the product of the number of layers and thethickness of each layer. After the layer increment exceeds the maximumacceptable amount, the build up level of the object would fall short ofthe amount predicted by the product of the number of layers and thethickness of each layer. Alternatively, the planarity of upper surfaceof the diagnostic part(s) may be lost (indicating that some droplocations may be receiving sufficient material while others are not). Byinspecting the diagnostic part(s), the maximum acceptable Z-incrementamount can be empirically determined. The optimal Z-increment amount canthen be selected as this maximum acceptable amount or it can be selectedat some thickness somewhat less than this maximum amount. Since it isknown that different build and support styles accumulate in the verticaldirection at different rates, the above test can be performed for eachbuild style and support style, wherefrom the optimal Z-increment for acombination of different styles can then be selected such that it is notthicker than any of the maximum amounts determined for each styleindividually.

Further, the dispensing head, in tracing a given scan line, may onlymaintain a substantially constant velocity over part of the scan line.During the remainder of the scan, the head 9 will either be acceleratingor decelerating. Depending on how the firing of the jets is controlledthis may or may not cause a problem with excess build up during theacceleration and deceleration phases of the motion. In the event thatvelocity changes can cause problem in a accumulation rate, the part orsupport building can be confined to the portion of the scan line overwhich the print head has a substantially constant velocity.Alternatively, as discussed in the concurrently filed U.S. patentapplication 08/722,326, a firing control scheme can be used which allowsaccurate deposition during the acceleration or deceleration portions ofa scan line.

As noted previously, in some preferred embodiments, the print head 9 isdirected to trace a raster pattern. An example of this is depicted inFIG. 6. As shown, the raster pattern consists of a series of rasterlines (or scan lines), R(1), R(2), . . . , R(N), running in theX-direction or main scanning direction and arrayed (i.e. spaced) alongthe Y-direction (i.e. the index direction or secondary scanningdirection). The raster lines are spaced from one another by a distanced_(r), which, in one preferred embodiment, is {fraction (1/300)} of aninch (about 3.3 mils or about 83.8 μm). Since the orifices of the printhead 9 are spaced by the distance d, which as discussed above ispreferably about 26.67 mils (0.6774 μm), and since the desired number ofraster lines may extend in the index direction by a distance greaterthan the length of the orifice plate 10, about 2.56 inches (65.02 mm),the print head 9 must be swept over the working surface through multiplepasses in order to trace out all desired raster lines.

This is preferably accomplished by following a two-step process. In thefirst step, the print head 9 is passed 8 times over the working surfacein the main scanning direction, with the Y-stage 16 a, 16 b beingindexed by the amount d_(r) in the secondary scanning direction aftereach pass in the main scanning direction. In the second step, theY-stage 16 a, 16 b is indexed by a distance equal to the length of theorifice plate 10 (2.5600 inches+d_(r) (0.0267 inches)=2.5867 inches(65.70 mm). This two-step process is then repeated until all of thedesired raster lines have been traced.

In a first pass, for example, the print head 9 might be directed totrace raster lines R(1) (via orifice 10(1) in FIG. 4), R(9) (via orifice10(2)), R(17) (via orifice 10(3)), etc. The Y-stage 16 a, 16 b wouldthen be directed to move the building platform 18 the distance d_(r)(one raster line) in the index direction. On the next pass, the printhead 9 might be directed to trace R(2) (via 10(1)), R(10) (via 10(2)),R(17) (via 10(3)), etc. Six more passes would then be performed with theY-stage 16 a, 16 b being indexed by the distance d_(r) after each pass,until a total of 8 passes have been performed.

After performing the first step (consisting of 8 passes), the secondstep is performed if there are more raster lines to be traced. Thesecond step consists of directing the Y-stage to move the buildingplatform by an amount equal to the full length of the orifice plate10+d_(r), 2.5867 inches (65.70 mm). As needed, another set of 8 passes,comprising the first step, is performed followed by another second step.The two-step process described above would then be repeated until allraster lines have been traced out.

An example of this two step process is depicted in FIG. 26 for a printhead consisting of two jets and wherein the two jets are separated onefrom the other by 8 raster spacings. The scanning of the cross-sectionsbegins with the first jet located at position 201 and the second jetlocated at position 301. The first step of the scanning process beginswith the scanning of raster lines 211 and 311 in the indicated directionby the first and second jets, respectively. As part of the first stepthe initial scanning of raster lines 211 and 311 is followed by an indexincrement of one raster line width as indicated by elements 221 and 321.Continuing as part of the first step, the initial raster scan and indexincrement are followed by seven more raster scans (depicted by pairs oflines 212 and 312, 213 and 313, 214 and 314, 215 and 315, 216 and 316,217 and 317, and 218 and 318) separated by six more 1 raster line widthindex increments (depicted with pairs of elements 222 and 322, 223 and323, 224 and 324, 225 and 325, 226 and 326, and 227 and 327).Immediately after scanning raster line pairs 218 and 318, the secondstep of the process is taken wherein the head is indexed in theY-direction according to the direction and lengths of raster lines 228and 229. The length of this index is equal to the head width (i.e. inthis example 8 raster lines widths) plus the width of 1 more rasterline. After this large increment, the first steps and second steps arerepeated as many times as necessary to complete the scanning of theparticular cross-section being formed. It will be apparent to one ofskill in the art that this two step scanning technique can beimplemented in other ways in alternative embodiments. For example thesecond step may, instead of consisting of the positive index incrementin Y as indicated by elements 228 and 328, consist of the large negativeincrement in Y as indicated by element 330 (i.e. three head widths minusone raster line width).

This preferred embodiment may be summarized as including the followingcharacteristics: 1) the spacing along an indexing direction betweenadjacent jets is an integral (N) multiple of the desired spacing (d_(r))between adjacent deposition lines which extend in a printing directionwhich is approximately perpendicular to the indexing direction; 2) thefirst step includes performing a number of passes (N) in the printingdirection where each pass is offset in the indexing direction by thedesired spacing (d_(r)) between adjacent deposition lines; and 3) thesecond step includes offsetting the print head 9 in the indexingdirection by a large amount such that the jets can deposit material inmaterial in another N passes, wherein successive passes are separated byone raster line index increments, and whereafter another large indexincrement will be made as necessary. In most preferred embodiments thesecond step index amount will be equal to the sum of the spacing betweenthe first jet and the last jet plus the desired spacing between adjacentdeposition lines (i.e., N×J+d_(r), where J is the number of jets on theprint head 9).

As noted in the above example, other second step index amounts arepossible. For example, negative second step increments (oppositedirection to the index increments used in the first step) equal to thesum of the head width plus the product of two times the width betweensuccessive jets less the width of one raster line spacing. In otherembodiments, it is possible to use second step index amounts which varyor which alternate back and forth between positive and negative values.In these embodiments the second step increment amount has the commonfeature that it is larger than the individual index amounts used in thefirst step.

In other preferred embodiments other single or multiple step indexingpatterns can be used, index direction increments could be generally bemade which include increments involving both negative and positivemovements along the Y-axis. This might be done to scan raster lines thatwere initially skipped. This will be described further in associationwith a technique called “interlacing”.

In some preferred embodiments, the firing of ink jets is controlled by arectangular bit map, i.e., pixel locations, maintained in the controlcomputer or other memory device. The bit map consists of a grid ofmemory cells, in which each memory cell corresponds to a pixel of theworking surface, and in which the rows of the grid extend in the mainscanning direction (X-direction) and the columns of the grid extend inthe secondary scanning direction (Y-direction). The width of (ordistance between) the rows (spacing along the Y-direction) may bedifferent from the width (or length of or distance between) of thecolumns (spacing along the X-direction) dictating that different dataresolutions may exist along the X and Y directions. In other preferredembodiments, non-uniform pixel size is possible within a layer orbetween layers wherein one or both of the pixel width or length isvaried by pixel position. In still other preferred embodiments, otherpixel alignment patterns are possible. For example, pixels on adjacentrows may be offset in the main scanning direction by a fractional amountof the spacing between pixels so that their center points do not alignwith the center points of the pixels in the neighboring rows. Thisfractional amount may be ½ so that their center points are aligned withthe pixel boundaries of adjacent rows. It may be ⅓, ¼ or some otheramount such that its takes two or more intermediate layers before pixelpatterns realign on subsequent layers. In further alternatives, pixelalignment might be dependent on the geometry of the object or supportstructure being dispensed. For example, it might be desirable to shiftpixel alignment when forming a portion of a support pattern that issupposed to bridge a gap between support columns or when forming adown-facing portion of an object. These and other alternative pixelalignment schemes can be implemented by modifying the pixelconfiguration, or alternatively, defining a higher resolution pixelarrangement (in X and/or Y) and using pixel firing patterns that do notfire on every pixel location but instead fire on selected spaced pixellocations which may vary according to a desired random, predetermined orobject biased pattern.

The data resolution in the main scanning direction can be defined interms of Main Direction Pixels (MDPs). MDPs may be described in terms ofpixel length or in terms of number of pixels per unit length. In somepreferred embodiments, MDP=300 pixels per inch (26.67 mils/pixel or677.4 μm/pixel). In other preferred embodiments, MDP=1200 pixels perinch. Of course any other MDP values can be used as desired. Similarlythe data resolution in the secondary scanning direction may be definedin terms of Secondary Direction Pixels (SDPs) and the SDPs may bedescribed in terms of pixel width or in terms of number of pixels perunit length. In some preferred embodiments SDP=MDP=300 pixels per inch(26.67 mils/pixel or 677.4 μm/pixel). The SDP may or may not beequivalent to spacing between raster lines and the MDP may or may not beequivalent to the spacing between successive drop locations along eachraster line. The spacing between successive raster lines may be definedas Secondary Drop Locations (SDLs), while spacing between successivedrop locations along each raster line may be defined as Main DropLocations (MDLs). Similar to SDPs and MDPs, SDLs and MDLs may be definedin terms of drops per unit length or drop spacing.

If SDP=SDL there is a one to one correspondence between data and droplocations along the secondary scanning direction and the pixel spacingis equal to that of the raster line spacing. If MDP=MDL there is a oneto one correspondence between data and drop locations along the mainscanning direction.

If SDL and/or MDL is larger than SDP and/or MDP, respectively, moredrops will need to be fired than that for which data exists, thus eachpixel will need to be used to control the dropping of more than onedroplet. The dispensing of these extra droplets can be done either bydispensing the droplets at intermediate points between the centers ofsuccessive pixels (i.e. intermediate dropping, “ID”) or alternatively,directly on top of pixel centers (i.e. direct dropping, “DD”). In eithercase this technique is called “overprinting” and results in faster buildup of material and eases mechanical design constraints involving maximumscan speeds and acceleration rates since the same Z-build up can occurwhile moving the print head and/or object more slowly. The difference inID overprinting versus non-overprinting, or DD overprinting, is depictedin FIGS. 16a to 16 d. FIG. 16a depicts a single drop 60 being depositedand an associated solidified region 62 surrounding it when the printhead is moving in direction 64. On the other hand, FIG. 16b depicts thesame region being cured but using the ID overprinting technique wheretwo drops 60 and 66 are deposited in association with the single datapoint when the head is moving in direction 64. The deposition zonefilled by the two drops is depicted by region 68. FIG. 16c shows asimilar situation for a four drop ID overprinting scheme wherein thedrops are indicated by numerals 60, 70, 66 and 72 and the depositionzone is depicted by 76 and wherein the scanning direction is stilldepicted by numeral 64. FIG. 16d depicts a similar situation for a lineof pixels 78, 80, 82, 84, 86 and 88 wherein numeral 90 depicts thelength of the deposition zone without overprinting and the numeral 92depicts the length of the deposition zone when using a four drop IDoverprinting technique. The above can be generalized by saying that IDoverprinting adds from approximately ½ to just under 1 additional pixellength to any region wherein it is used. Of course, the moreoverprinting drops that are used, the more vertical growth a pixelregion will have.

If SDL and/or MDL is less than SDP and/or MDP, respectively, drops willbe fired at fewer locations than those for which data exists, at leastfor a given pass of the print head. This data situation may be used toimplement the offset pixel and/or non-uniform sized pixel techniquesdiscussed above.

An N row by M column grid is depicted in FIG. 7. As shown, the rows inthe grid are labeled as R(1), R(2), . . . , R(N), while the columns inthe grid are labeled as C(1), C(2), . . . , C(M). Also shown are thepixels making up the grid. These are labeled as P(1,1), P(1,2), . . . ,P(M,N) .

To build a cross-section, the bit map is first loaded with datarepresentative of the desired cross-section (as well as any supportswhich are desired to be built). Assuming, as with some preferredembodiments, a single build and support material is being used. If it isdesired to deposit material at a given pixel location, then the memorycell corresponding to that location is appropriately flagged (e.g.loaded with a binary “1”) and if no material is to be deposited anopposite flag is used (e.g. a binary “0”). If multiple materials areused, cells corresponding to deposition sites are flagged appropriatelyto indicate not only drop location sites but also the material type tobe deposited. For ease of data handling, compressed data defining anobject or support region (e.g. RLE data which defines on-off locationpoints along each raster line as described in concurrently filed U.S.patent application Ser. No. 08/722,326, now U.S. Pat. No. 5,943,235) canbe Booleaned with a fill pattern description (e.g. Style fileinformation as described in U.S. Pat. No. 5,943,235) to be used for theparticular region to derive a final bit map representation used forfiring the dispensing jets. The actual control of the jets may begoverned by a subsequently modified bit map which contains data whichhas been skewed or otherwise modified to allow more efficient datapassing to the firing control system. These considerations are discussedfurther in the U.S. patent application based on 3D Systems' U.S. Pat.No. 5,943,235. The raster lines making up the grid are then assigned toindividual orifices in the manner described earlier. Then, a particularorifice is directed to fire or not at firing locations corresponding todesired drop locations or pixel locations depending on how thecorresponding cells in the bit map are flagged.

As discussed above, the print head 9 is capable of depositing dropletsat many different resolutions. In some preferred embodiments of thepresent invention SDP=SDL=300 pixels and drops per inch. Also in somepreferred embodiments, MD L is allowed to take on three different valueswhile MDP remains fixed 1) MDL=300 drops per inch and MDP=300 pixels perinch; 2) MDL=600 drops per inch; and MDP=300 pixels per inch or 3)MDL=1200 drops per inch and MDP=300 pixels per inch. When the MDL to MDPratio is greater than one, the extra drops per pixel are made to occurat intermediate locations (ID overprinting) between the centers of thepixels. With the currently preferred print head and material, the volumeper drop is about 80 to 100 picoliters which yields roughly drops havinga 2 mil (50.8 μm) diameter. With the currently preferred print head, themaximum frequency of firing is about 20 kHz. By way of comparison, afiring rate of 1200 dpi at 13 ips involves a firing frequency of about16 kHz, which is within the permissible limit.

In some preferred embodiments, build styles are defined separately fromobject data for ease of data manipulation, transfer and memory loading.In this regard, as noted above, data descriptive of the object isBooleaned (e.g. intersected) together with information descriptive of abuild style, on a pixel by pixel basis, to yield a pixel by pixelrepresentation of the deposition pattern at any given location. Forexample, if a completely solid pattern is to be dispensed in two passes(e.g. a two step pattern), the object data would first be Booleaned(e.g. intersected) with a first build style pattern representing theportion of the pixels at which drops are to be deposited (or for ease ofterminology we may say “exposed” in analogy to the selectivesolidification that is used in photo-based stereolithography). Theresultant modified pixel data could thereafter be used to control jetfiring. Next, the object data would be Booleaned (e.g. intersected) withthe complementary build style pattern to yield modified pixel data forcontrolling a second firing of the jets. In other preferred embodiments,object data and support data can be immediately correlated to buildstyle data upon its derivation. In further preferred embodiments, buildstyle information could also include pixel shifting information, pixelsizing information, overprinting information, scan direction preferencesfor depositing on each pixel location, planarization direction androtational preferences, and the like. The build styles described hereinenhance system performance by: 1) enhancing build speed; 2) enhancingaccuracy of the formed object; 3) enhancing surface finish; 4) reducingstress in the object and/or distortion of the object; or 5) acombination of one or more of these simultaneously.

A significant problem with Selective Deposition Modeling systemsinvolves ensuring the reliability of material deposition and moreparticularly of achieving uniform thickness of deposited cross-sections.Another problem involves achieving a uniform thickness for all buildstyles. In ink jet systems this reliability problem can take the form,inter alia, of misfiring or non-firing jets. In a multijet system,further problems exist regarding non-unifeormity of jet firingdirection, non-uniformity of dispensed volume between jets, and to alesser extent, non-uniformity of dispensed volume from a single jet overtime.

The problem of non-uniformity of cross-section thickness can also resultfrom other phenomena as well. As an example, once a droplet leaves a jetthere is a time of flight before the droplet encounters the workingsurface. When leaving the jet, the drop is fired with an initialdownward velocity component away from the jet but since the jet ismoving in the main scanning direction the droplet also has a horizontalvelocity component. Once the droplet leaves the jet it is subject tovarious external and internal forces including gravity, viscous dragforces and surface tension. These initial conditions and forces in turnlead to the conclusion that the droplet may not, and probably will not,land directly on the working surface below the position from which itwas fired. Instead the droplet will land somewhat away from thistheoretical drop point, typically in the direction of travel of theprint head. In other words the firing location and impact (or drop)location will not have the same XY coordinates but instead will beshifted one from the other. The shift in horizontal distance that occursdepends on the above noted factors but also on the distance between theorifice plate 10 and the vertical position (e.g. “Z” position) of theworking surface at each horizontal location (e.g. X and/or Y position).As noted above variations in vertical position can occur for a number ofreasons. For example, variations can result from differences in geometrybetween different portions of a cross-section (more or less materialspreading results in less or more deposition thickness). As anotherexample, variations can result from the temporal ordering of depositionfor a given spatial pattern (previously deposited material on anadjacent pixel site can limit the ability of the material to spread inthat direction).

As noted previously, the preferred system for embodying this inventionutilizes planarization to bring each deposited cross-section to auniform height wherein the net layer thickness results from thedifference in Z-level between the planarization levels of twoconsecutive layers. In turn, if it is desired that the planarizationstep form a completely smooth and uniformly leveled layer, the Zincrement between planarizations must be at or below the minimumdeposition/build up thickness for each point on the entire layer. If onejet is weakly firing (or not firing), the minimum thickness build up canresult in net layer thicknesses much smaller (i.e. near zero or zero)than desired and therefore much longer build times than desired. Severaltechniques for dealing with these deposition/build up problems aredescribed herein. Other preferred embodiments might involve the use ofplanarization on periodic layers instead of on every layer. For exampleplanarization may be used on every second, third, or other higher orderspaced layer. Alternatively, determination of which layers or portionsof layers to planarize may be based on object geometry.

Time of Flight Correction

As noted above, one difficulty in ensuring that the droplets strike thedesired locations on the working surface involves the time that thedroplets are in flight (i.e. the time of flight of the droplets). If thetimes of flight were always the same and if the direction and amount ofoffset were always the same there would be no time of flight issue sincethe only effect would be a shift between firing coordinates anddeposition coordinates. However, when forming three-dimensional objectsit is typically desirable to jet material when the head is traveling inboth the positive and negative main scanning directions (and may eveninvolve, for example, alternating the definitions of main and secondaryscanning directions). This results in a change in offset direction (e.g.reversal of offset direction) between scans due to relative movementoccurring in different directions (e.g. opposite direction). Thisproblem can be readily addressed by causing firing signals to occurbefore the head actually reaches the point directly above the desireddeposition site. This correction to firing time is known as the “time offlight correction”. The time of flight may be corrected by utilizationof a correction factor applied to scanning in each direction separatelyor alternatively a single correction factor may be used to bringdeposition from one scanning direction into registration with theuncorrected scans made in the other direction. The time of flightcorrection may be implemented in a number of ways. One way, for exampleis by appropriately defining the initial firing location (X position) atthe beginning of each raster line, which initial firing location will beused to set the firing locations for all other pixels along the rasterline.

FIGS. 27a-27 e illustrate the relationships between firing location,drop location, and time of flight wherein like elements are referencedwith like numerals. FIG. 27a illustrates the situation where firinglocations 404 a and 404 b are both coincident with desired drop location402 (i.e. no time of flight correction factor is used). Element 404 arepresents the firing location when the head is passing in the positiveX-direction, represented by element 406 a, and element 404 b representsthe firing location when the head is passing in the negativeX-direction, represented by element 406 b. Elements 408 a and 408 brepresent the nominal path followed by the droplets after leaving firinglocations 404 a and 404 b, respectively. The nominal paths 408 a and 408b direct the droplets to actual drop locations 410 a and 410 b, wherethe droplets impact the surface and form impacted droplets 412 a and 412b. The crossover point (i.e. focal point) for the droplets fired, whilescanning in both directions, is depicted with numeral 414. The planedefined by the crossover points for the entire layer may be called thefocal plane. Elements 416 a and 416 b represent the time of flightfactor used in terms of an X-displacement between the firing locationsand the desired drop location. Whether or not the actual drop locationsmatch the desired drop location determines the appropriateness thecorrection factor. In FIG. 27a it can be seen that the droplets aremoving in diverging directions and that the impacted droplets do notoverlap at the working surface resulting in a minimal build up in Z andinaccurate XY placement of material. FIG. 27b represents the situationwhere a small time of flight correction factors 416 a and 416 b are usedwhich result in a focal point located above the desired working surfaceand in a closer spacing of the impacted droplets 412 a and 412 b ascompared to that depicted in FIG. 27a. If the time of flight correctionwere any larger, Z build up would be increased due to the overlap orsuperposition of impacted droplets 412 a and 412 b. FIG. 27c representsa situation where the time of flight correction factors used result inthe most accurate placement of impacted droplets 412 a and 412 b(assuming the thickness of impacted droplet 412 a is small compared tothe drop distance 418 and that the angle of incidence is not too large).If optimal time of flight correction is based on maximum Z accumulationthen FIG. 27c depicts the optimal situation. FIG. 27d represents thesituation where the time of flight correction factors 416 a and 416 bare slightly larger than those used in FIG. 27c but still result inZ-accumulation based on the superposition of both droplets. TheX-direction placements of the droplets are still reasonably accurate andthe focal point 414 of dispensing is somewhat below the desired workingsurface (and actual working surface). FIG. 27e represents the situationwhere even larger time of flight correction factors are used such thatZ-accumulation is reduced to a minimal amount and where the focal pointis even further below the desired working surface.

If drag effects and gravitational effects on flight time are ignored,the time of flight correction value (time) would be equal to thedistance (length) separating the orifice from the working surfacedivided by the downward velocity (length/time) at which the droplet isdispensed. However, it is believed that drag is an important factor. Forexample, in some preferred embodiments print head scanning speed isapproximately 13 inches per second, the distance from the orifice plateto the working surface is approximately 0.020 inches, and the initialvertical firing speeds are believed to be on the order of 200 to 360inches per second. If drag or other frictional forces are ignored, underthese initial conditions, a shift between firing locations and droplocations of approximately 0.8 to 1.3 mils would be expected. However,under these conditions, in practice shifts in the main scanningdirection between the firing location and drop location of approximately2 mils have been observed.

The appropriate correction value can be readily determined empiricallyby attempting to deposit droplets at a single X location when scanningin both directions and reiterating the experiment with differentcorrection values until the two drops land at the same point. As notedabove, in some preferred embodiments the most appropriate time of flightcorrection value is the one for which the droplets hit the sameposition. In terms of the above example, if drag forces are ignored,time of flight correction factors of approximately 60 to 100 μS would beexpected. When in practice correction factors of approximately 150 to200 μS have been found to be more appropriate.

In other preferred embodiments the optimal time of flight correctionfactor is not set at a value which yields the most accurate targeting(i.e. the focal point is not at the working surface) but instead is setat a value which would yield most accurate targeting some distance belowthe actual working surface (i.e. the focal point is located below theworking surface). These embodiments may be called “off surfacetargeting” embodiments. In this context, most accurate targeting isconsidered to occur when vertical accumulation rate is the greatest andprobably when the X position is most precisely impacted. FIG. 27ddepicts an example of targeting for these off surface targetingembodiments. These off surface targeting embodiments are believed to beparticularly useful when building is to occur without the use ofadditional components for maintaining the desired and actual workingsurface at the same level (e.g. without a planarizer or withoutadditional elements such as a surface level detection device andadjustment mechanisms or schemes).

A characteristic of these off surface targeting embodiments is thatZ-accumulation is self-correcting or self-compensating. As long as theZ-increments between deposition of successive layers are within anappropriate range and the deposition pattern allows horizontal spreadingof dispensed material instead of only vertical accumulation, excessZ-accumulation on one layer causes a reduction in Z-accumulation on oneor more subsequent layers causing the net accumulation to maintain thefocal point somewhat below the actual working surface. On the otherhand, again as long as Z-increments between deposition of successivelayers is within an appropriate range and the deposition pattern allowshorizontal spreading of dispensed material instead of only verticalaccumulation, too little Z-accumulation on one layer causes an increasein Z-accumulation on one or more subsequent layers thereby causing netaccumulation to maintain the focal point somewhat below the actualworking surface. The preferred Z-increment range is discussed furtherbelow.

This self-correcting aspect can be understood by studying and comparingFIGS. 27c, 27 d and 27 e. When deposition begins (e.g. at the platform)the time of flight correction factor(s) are chosen such that the focalpoint is somewhat below the actual working surface as depicted in FIG.27d (i.e. the focal point should be set at an appropriate position suchthat the situations depicted in FIGS. 27c and 27 e do not occur). Ifwhen forming the first layer, too little material is deposited, for thegiven Z-increment being used, the actual surface will be lower ascompared to the repositioned focal plane (but will still be above it aslong as the Z-increment was not too large). This results in a moreoptimally focused deposition when forming the next layer, this in turnresults in an increase in deposition thickness as depicted in FIG. 27c.If the net Z-accumulation resulting from depositing the second layer isstill too low (as compared to the two Z-increments made), then the nextlayer when being deposited will have an actual surface which closer tothe optimal focus plane than the original surface was. This closerapproach to optimal positioning results in increased Z-accumulationwhich will again drive the net accumulated thickness toward thatrequired by the Z-increments. On the other hand, if net accumulationfrom depositing the second layer is greater than that dictated by thetwo Z-increments, then the actual working surface will be further awayfrom the focal plane and less Z-accumulation, upon forming the nextlayer, will occur thereby driving the net accumulation toward the amountrequired by the Z-increments. This is the situation depicted in FIG.27e.

When the focal plane is appropriately below the actual working surface,when the z-increment amount is appropriately selected to approximatelymatch deposition rates, and when objects/supports are being formed in anon-solid manner (not all pixel locations are directly deposited on, thesystem is stabilized and both supports and objects can be formed withaccurate vertical dimensions without the explicit need of a planarizer.Of course a planarizer can still be used if desired. For optimaloperation of these embodiments it is preferred that the Z-incrementshould be selected to be between the average amount accumulated perlayer during optimal targeting (e.g. FIG. 27c) and the average amountaccumulated when no superposition occurs (e.g. FIG. 27e). It is furtherpreferred that layer thickness be significantly less than the distancethat separates the plane of optimal focus (e.g. FIG. 27c) from the planewhere superposition no longer occurs (e.g. FIG. 27d).

As noted above, in some of these embodiments objects may be formed insuch a manner as to allow regions for material to spread horizontallyinstead of just accumulating vertically, based on the level of targetingoptimization, and thereby allowing self correction of Z-accumulation.One such embodiment might involve the forming the object as acombination alternating solid layers and checkerboard layers. Other suchembodiments might involve the formation of solid outward facing surfacesand checkerboard, offset checkerboard, or other open structures ininternal object regions. Other appropriate building patterns can bedetermined empirically by building and analyzing test parts.

In some of these offset surface targeting embodiments, the mostpreferred initial target surface/focal plane position is selected to beapproximately in the middle of the situations depicted in FIGS. 27c and27 e. One way of accomplishing this is to ignore the hypothetical focalpoints and instead focus on time of flight values. The time of flightcorrection values may be selected so that they are greater than theoptimal time of flight correction values (as discussed above) and lessthan the time of flight correction values which yields immediatelyadjacent but non-overlapping (i.e. non-superimposed) impact zones. Mostpreferably the selected time of flight values would be taken asapproximately the average of these two extremes.

Some offset surface targeting embodiments might be used tosimultaneously form different portions of objects and/or supports suchthat their upper surfaces are intentionally at different heights afterformation of any given layer. These different height embodiments mightbenefit from utilization of data manipulation techniques, like the SMLCtechniques, discussed in previously referenced U.S. Pat. No. 5,999,184as well as some of the of the other previously referenced U.S. patentsand applications.

In addition to the above noted time of flight issues, other issues arisethat can be corrected using modified time of flight correction factors.For example, when using ID overprinting techniques to cause more buildup, features on scan lines which are scanned in opposite directions willlose alignment since the feature will be extended in one direction onone line and in the other direction on another line. This situation isdepicted in FIGS. 17a and 17 b. FIG. 17a depicts two points 60 and 100belonging respectively to scan lines traversed in directions 64 and 104.Regions 62 and 102 depict the extents of deposited material associatedwith points 60 and 100, respectively. FIG. 17b depicts the same points60 and 100 where jetting occurs using four times overprinting (i.e. fourdroplet depositions per pixel). Extents of deposition are depicted withnumerals 76 and 106 respectively. As can be seen, due to the differentdirections of overprinting, registration between the physical featureson the two lines is lost. The above mis-registration can be corrected byan additional time of flight correction factor which can be empirically,or possibly theoretically determined so as to cause realignment offeatures on different scan lines. Of course this form of correction doesnot account for any extra length added to object features along thescanning lines.

A different form of correction that can avoid both problems is proposedwhich involves recognition that a given pixel is not bounded on its farside, in the scanning direction, by an adjacent pixel that also callsfor material deposition. Based on this recognition, no overprinting isused on such an unbounded pixel. As another alternative, the extra linelength might be compensated for by using a form of drop widthcompensation similar to line width compensation used in photo-basedstereolithography and as described in the previously referenced U.S.Pat. Nos. 5,854,748 and 5,870,307 but applied only to the points alongeach scan line representing a transition from deposition to nodeposition. As an approximate correction these “terminal points” couldsimply be deleted from the deposition pattern as they will be in therange of ½ to fully covered by the use of ID overprinting of immediatelyadjacent pixels. Another variant involves the use of shifted time offlight correction data to implement subpixelling deposition.

The time of flight correction factors may also be used in variantmanners for somewhat opposite purposes to those described above. Inthese embodiments, time of flight correction factors may be used todeposit material at intermediate pixel (i.e. subpixel) locations forimplementation of enhanced building techniques. These enhanced buildingtechniques might involve formation of down-facing surfaces, formationand placement of supports, enhanced vertical build up of material,enhanced resolution, and the like. In preferred embodiments, enhancedobject formation may be achieved in a single pass or multiple passimplementations.

Droplet Width Compensation

In some situations it may be desirable to modify the object data byperforming droplet width compensation (i.e. deposition widthcompensation). Compensation (by offsetting inward toward solid one ormore full pixel widths) can be used to achieve enhanced accuracy if thedrop width is at least somewhat greater than the pixel width and/orlength. This technique may be used in combination with any of theembodiments described above or any embodiments described herein after.As the drop width approaches or exceeds twice the pixel width (and/orlength) better and better accuracy can be obtained by a single ormultiple pixel offset. Droplet width compensation may be based ontechniques like those disclosed in U.S. Pat. Nos. 5,854,748 and5,870,307. Alternatively they may involve pixel based erosion routines.In some embodiments the pixel based erosions might involve multiplepasses through a bit map wherein “solid” pixels meeting certain criteriawould be converted to “hollow” pixels.

Some embodiment might involve the following steps wherein each edge ofthe bit map is: 1) In a first pass through the bit map all “solid”pixels which are bounded on their right side by a “hollow” pixel areconverted to “hollow” pixels; 2) In a second pass all “solid” pixelswhich are bounded on their left side by a “hollow” pixel are convertedto “hollow” pixels; 3) In a third pass all “solid” pixels which arebounded on their upper side by a “hollow” pixel are converted to“hollow” pixels; and 4) In a fourth pass all “solid” pixels which arebounded on their lower side by a “hollow” pixel are converted to“hollow” pixels. Other embodiments might change the order of steps (1)to (4). If more than a one pixel erosion is required, steps (1) to (4)can be repeated as multiple times until the correct amount of reductionis achieved. These embodiments can perform a reasonable droplet widthcompensation; however, they suffer from the short coming that pixels insolid corner regions (whether an object corner or an object edge thatdoes not run parallel to either the X or Y axis) are removed at a fasterrate than pixels in which represent boundary regions that are parallelto either the X or Y axis.

Other embodiments which attempt to address these differentials inerosion rate might involve steps as follows: 1) In a first pass throughthe bit map all “solid” pixels which are bounded on their right side bya “hollow” pixel and all other sides by “solid” pixels are converted to“hollow” pixels; 2) In a second pass all “solid” pixels which arebounded on their left side by a “hollow” pixel and on all other sides by“solid” pixels are converted to “hollow” pixels; 3) In a third pass all“solid” pixels which are bounded, on at least their upper side, by a“hollow” pixel are converted to “hollow” pixels; and 4) In a fourth passall “solid” pixels which are bounded, on at least their lower side, by a“hollow” pixel are converted to “hollow” pixels. Other embodiments mightchange the order of steps (1) to (4) or the conditions on whichconversion will be based. If more than a one pixel erosion is required,steps (1) to (4) can be repeated as multiple times until the correctamount of reduction is achieved. These embodiments do a better job ofminimizing excess reduction in corner regions.

Other embodiments, might involve setting erosion conditions based onwhether or not two, three or all four sides of a pixel are bounded by“hollow” pixels. Other embodiments may vary the erosion conditionsdepending on how many times the bit map has been passed through. Otherembodiments may use a combination of erosions and Boolean comparisonswith original cross-section or other partially compensated bit maps toderive final bit map representations of the pixels to be exposed.Numerous other embodiments and algorithms for eroding pixels whileemphasizing the reduction or maintenance of certain object features willbe apparent to those of skill in the art in view of the teachingsherein.

In situations where X and Y pixels dimensions are significantlydifferent, droplet width compensation may only be necessary along oneaxis instead of both axes. In these situations, embodiments similar tothose described above may be used wherein only a portion of the stepswill be performed per erosion. It is anticipated that deposition widthcompensating schemes can also be utilized using subpixel offset amountsin either one or both of the X and Y dimensions.

Randomization

A technique (method and apparatus) known as randomization can beemployed in the build process. This technique may be used in combinationwith any of the embodiments described above or any embodiments describedherein after. According to this technique, the manner of dispensingmaterial at each location for two consecutive cross-sections is varied.This can lead to a more uniform build up of material across a layer(i.e. lamina) resulting in the ability to potentially use thickerlayers, thus improving build time. This technique also minimizes theeffects from any single jet or plurality of jets that may not beproperly firing. The varying of deposition can occur in several ways.For example variation may occur by: 1) varying the jet which depositsmaterial onto a given portion of a layer relative to the jet thatdeposited material on the corresponding portion of the immediatelypreceding layer; 2) varying the temporal order or spatial order ofdispensing onto any given portion of the layer relative to any otherportion of the layer; and 3) a combination of these, such as varying themain scanning orientation or direction and/or varying the secondaryscanning orientation or direction. The varying of deposition from layerto layer can occur in a totally random manner or it can occur in aperiodic or planned manner. A similar technique has been used inphoto-based stereolithography though for a completely different purpose(see Alternate Sequencing in previously referenced U.S. Pat. No.5,711,911).

Specific embodiments for varying the deposition will now be given. Thepresently preferred randomization technique maintains the orientation ofthe main and secondary scanning directions but uses a differentdispenser (e.g. jet) to deposit material along corresponding scanninglines between two layers. In other words, a first dispenser is used toscan a particular main scanning line on a first layer and a seconddispenser may be used to scan that particular main scanning line on asubsequent layer (the one immediately above the particular scanning lineon the first layer). In some preferred embodiments, a particular scanline is exposed (i.e. deposited on), from layer-to-layer, using adifferent jet until 96 layers have been deposited and each of the 96jets has deposited on the particular scan line, after which the processrepeats. These embodiments are examples of “full head” randomization. Inother preferred embodiments, “half head” randomization is preferred.Half head randomization can reduce the number of passes that must bemade over the any cross-section depending on the object geometry. Basedon building with the presently preferred 96 jet head, half headrandomization involves scanning over any given location with randomizeddispensing occurring from either jets 1 to 48 or jets 49 to 96.

To explain the full head randomization embodiments in more detail,reference is made to FIGS. 4a and 6. For a particular layer, orifice10(1) might be used to trace scan lines R(1)-R(8); orifice 10(2), linesR(9)-R(16); orifice 10(3), lines R(17)-R(25); orifice 10(4), linesR(26)-R(33), etc. On the next layer, however, these assignments arechanged such that a given orifice does not trace the same scan line onthe next layer. For example, the following new assignments might bemade: orifice 10(1), lines R(257)-R(264); orifice 10(2), linesR(265)-R(272); orifice 10(3), lines R(273)-R(280), etc.

Another embodiment might involve relatively rotating the partiallyformed object and/or the print head by some amount (e.g. 30°, 60°, or90°) between the deposition for two layers so that the main andsecondary scanning orientations are changed from their previousorientations. This results in material deposition on a current layer,(i.e. lamina), from any jet, mainly occurring above material which wasdeposited by other jets on the previous layer. This is depicted in FIG.8 wherein the scan lines associated with a first layer are depicted bylines R₁(1), R₁(2), R₁(3), R₁(4), . . . ,R₁(N-3), R₁(N-2), R₁(N-1),R₁(N) while the scan lines associated with a subsequent layer aredepicted by line R₂(1), R₂(2), R₂(3), R₂(4), . . . ,R₂ (N-3), R₂(N-2),R₂(N-1), R₂(N) which are rotated by 90° with respect to the scanninglines of the first layer. The amount of rotation may vary betweensubsequent layers or it may be a constant amount. The angles may bechosen such that if the rotation is continued for a sufficient number oflayers, identical jets will deposit material over identical scan lineswhere deposition occurred on previous layers. Alternatively, the anglesmay be chosen so that no identical jet to scan line redeposition occurs.

Additional embodiments might involve changing the order of progressionfrom one scan line to another (in the secondary scanning direction).This is depicted in FIG. 9, where for a first layer the order ofdeposition of material on main scan lines begins on the upper most scanline, R₃(1) and proceeds to scan lines R₃(2),R₃(3), . . . ,R₃(N-2),R₃(N-1), and ends with lower most scan line R₃(N). The order ofprogression of scan lines is depicted by arrow R_(3P). The deposition ofmaterial on scan lines for a subsequent layer begins on the lower mostscan line, R₄(1) and proceeds to scan lines R₄(2), R₄(3), . . . ,R₄(N-2), R₄(N-1), and ends with upper most scan line R₄(N). The order ofprogression of scan lines on this subsequent layer is in the oppositedirection to that of the lines on the first layer and is depicted byarrow R_(4P.)

Additional embodiments are depicted in FIGS. 10a and 10 b, wherein thedirection of scanning along corresponding scan lines is reversed betweentwo subsequent layers. FIG. 10a depicts the scanning directions for scanlines on a first layer wherein scan lines R₅(1) and R₅(3) are scannedfrom left to right and scan line R₅(2) is scanned from right to left.FIG. 10b depicts that the scanning directions are reversed on asubsequent layer wherein scan lines R₆(1), R₆(2), and R₆(3) overlayR₅(1), R₅(2), and R₅(3), respectfully, and wherein scan lines R₆(1) andR₆(3) are scanned from right to left and scan line R₆(2) is scanned fromleft to right.

Many other randomization patterns are possible including combinations ofthe above described techniques. Depending on the randomization techniquechosen, the randomization process may cause an overall increase in layerdeposition time since it might result in the need to perform additionalmain scanning passes. However, this possible disadvantage is believed tobe outweighed by the enhancement in uniform layer build up.Additionally, since heat removal is a significant problem when usingelevated dispensing temperatures (as used to make the materialflowable), these extra passes can be effectively used to allowadditional cooling to occur prior to deposition of a subsequent layer.

Drop Location Offsetting

As noted above some building techniques can be enhanced by the use ofoffset scan lines and/or offsetting of drop locations along scan lines.These offsetting techniques could be used in combination with the abovenoted randomization techniques, though it should be understood thatcorresponding lines and drop locations on successive layers may beoffset from one another. These techniques may also be used incombinations with other embodiments disclosed herein before or hereinafter. In some preferred embodiments this offsetting may be up to ½ theline spacing or drop spacing. One use of offset pixelling might involvedeposition of material on a down-facing portion of a cross-section so asto aid in bridging the gap between adjacent support elements. In factthe down-facing region may be cured in multiple passes whereinprogressive or alternating offset, between successive passes, are usedto bridge a wide gap between support elements. In these embodiments anynon-down-facing portion of the cross-section might be exposed using oneor more depositions and offset or non-offset pixels and deposition inany down-facing portion might occur by multiple depositions (orexposures) where pixels zones partly overlap. The overall height ofdeposition, in preferred embodiments, might be made uniform by trimmingto an appropriate level by planarizing.

In some embodiments, offsetting of pixels and therefore drop sites mightoccur during support structure formation to enhance the formation ofarch-like supports, bridges, or branching supports (e.g. like limbs of atree). In some embodiments, offsetting of pixels might occur duringobject formation to enhance building of object sections which protrude alimited amount beyond the boundaries of the immediately preceding objectlamina. Protruding supports and object portions can be formed withoutthe use of offset pixelling but it is believed that offset pixelling canbe useful to aid in the formation of such structures wherein lessmaterial may slump into regions below the layers levels at which it wasdispensed.

Embodiments may involve the offsetting of pixels on every layer oralternatively may involve the offsetting of pixels only on periodiclayers. In this last alternative, material is deposited according to thesame pixel positions over a number of layers. According to thisalternative, stabilization of overhanging regions may be allowed tobetter occur by build up of multiple layers, above an initial overhang,prior to attempting the formation of a subsequent overhang.

The offsetting of pixels, e.g., to build branching supports or taperingoutward object structures, results in the formation of structures whichbranch out over empty space. The extent of this branching is limited tosome thing less than one droplet width per layer. Whether each layerextends beyond the boundary of its immediately preceding layer, orwhether multiple layers are built above one another followed by periodicextensions beyond the boundary of an immediately preceding layer, onecan define an angle of extension based on the average extension over anumber of layers. The maximum angle of extension depends, in part, onthe rate at which the material near and in the extended portionsolidifies, which in turn depends on the amount of material dispensednear and in the extended portion. The layers can be built at any anglewherein the material solidifies quickly enough and is capable ofsupporting the next layer of material. In some preferred embodiments,extension angles close to 30 degrees have been achieved. It is believedthat extension angles approaching or even exceeding 45 degrees arepossible.

Due to material cool down rates, it is preferred that the formation ofoverhanging solid object portions be achieved in multiple passes. In onepreferred embodiment, the extension region is deposited on one or moreinitial passes and the fully supported regions are exposed on one ormore subsequent passes. This embodiment allows the material in theextension regions to cool and solidify without the added delays thatmight be associated with heat absorption from material dispensed in theinterior regions. In another preferred embodiment, the interior of thelayer is exposed initially and the extension regions are exposed in oneor more subsequent passes. This embodiment allows time for the materialon the interior portions to cool somewhat prior to dispensing theextension regions thereby reducing the risk of the extension materialremaining flowable for too long a time. For a given set of buildparameters, the useable extension angles can be empirically determinedby building and examining test parts.

Offsetting of pixels may be used in combination with multiple passesover a given portion of a layer so as to allow build up of materialaround a given geometric feature in a prescribed order and offsetpattern. For example, offsetting may occur on one side of a feature suchthat a fraction of a pixel shift in position occurs away from that sideof the feature, while a different offset might be used so that the samefractional shift might be obtained in the opposite direction on theopposite side of the feature.

An alternative to offset pixelling is simply to build objects usinghigher resolution data and associated build patterns or styles thatyield the desired drop density which may be less than that providedinherently by the data but which still may yield formation of solidstructures or other desired features.

Scan Line Interlacing:

Interlacing is another technique that can be used to enhance objectformation. As with all other embodiments disclosed herein, theembodiments of this section are combinable with the other embodimentsdisclosed herein. As discussed previously, if the head is not orientedat the saber angle, the spacing between the jets is not equal to thedesired resolution and thus is not equal to the desired spacing of mainscanning or raster lines. As such, by its nature, a form of main scanline interlacing must be used if it is truly desired to deposit materialalong all main scan lines. However, additional interlacing may be donefor a number of reasons (e.g. to enhance layer cooling and/or materialbuild up).

A variety of scan line interlacing patterns can be used, whether or notthe print head is oriented at the saber angle, whether or not thepreferred raster scanning technique is used, whether or not a vectorscanning technique is used, whether or not some other scanning techniqueor combination technique is being used.

In one preferred embodiment, as previously described, the head isoriented perpendicular to the main scanning direction and a resolutionof 300 scan lines per inch is used. In this configuration successivejets are spaced {fraction (8/300)} of an inch apart. The head is made toperform 8 main scans, the first 7 of which are followed by a secondaryscan of width equal to the spacing between the raster lines (rasterwidth), and the eighth of which is followed by a secondary scan of widthequal to the effective head width plus the raster width. Repetitions ofthe above scanning pattern are made until the width incremented in thesecondary scanning direction has equaled or exceeded the width of thebuilding region.

Alternative embodiments could limit the X range of main scanning to thatwhich is sufficient to effectively cover the working region required bythe object, by the particular object cross-section being scanned, byeach segment of the object length required to make the 8 closely spacedmain scans, or by other schemes which lead to a reduction in scanningtime. Similarly, the positioning along the secondary scanning axis couldlikewise be limited to the width and position of the object,cross-section being scanned, particular portion of a cross-section beingscanned, or the like. In preferred embodiments, the use of randomizationmay increase the amount of indexing needing to be performed so that theappropriate jets may trace the appropriate main scan lines. Otherembodiments may limit the main scanning to paths which actually includeactive drop locations.

As a first preferred alternative interlacing technique non-adjacent scanlines would be left unexposed after at least a first pass whereafter onone or more subsequent passes the intermediate lines would be exposed.In other preferred embodiments, it is desired that intermediate rasterlines be drawn prior to depositing material on either adjacent rasterline or after depositing material on both adjacent lines. Examples ofthis type of embodiment are depicted in FIGS. 11a, 11 b, and 22 a-22 d.FIGS. 11a and 11 b depict the situation wherein every other line isskipped on a first pass. FIG. 11a depicts four scanning lines whereintwo lines are to be exposed (i.e. the drop locations to be used) on afirst pass. FIG. 11b depicts the same four scanning lines wherein theother two lines are to be exposed (i.e. the drop locations to be used)on a second pass. Further examples of interlaced patterns are shown inFIGS. 22a-22 d. In these figures two headed arrow 30 represents the mainscanning direction, spacing d_(r) represents the spacing betweensuccessive raster lines, and for clarity, the beginning points and endpoints of the lines are shown offset although in practice the lineswould have the same beginning and ending points. FIG. 22a depicts aseries of raster lines to be scanned in the main scanning direction.FIG. 22b depicts first raster lines 32 to be exposed on a first pass andsecond raster lines 34 to be formed on a second pass according to theexample of FIGS. 11a and 11 b. FIG. 22c depicts raster lines 32, 34, 36and 38 to be exposed on first, second, third and fourth pass,respectively. FIG. 22d depicts raster lines 32, 34, 36, 38, 40, and 42to be exposed on first, second, third, fourth, fifth and sixth pass,respectively. In the example of FIG. 22d other raster line scanningorders could also be used while still ensuring that when intermediatelines are deposited they are either not bounded on either side or thatthey are bounded on both sides by previously deposited adjacent rasterlines. For example, other useful scanning orders might be 32, 34, 38,36, 40 and 42; 32, 36, 34, 40, 38 and 42; or the like.

In one preferred system, to fully implement these embodiments in ageneralized manner using a minimum number of passes, an odd number ofraster lines would need to exist between the line scanned by one of thejets (e.g. a first jet),and the line scanned by an adjacent jet (e.g. asecond jet). In other words, the number of d_(r) spacing betweensuccessive jets would have to be even; thereby requiring that twoadjacent jets must be positioned so as to scan raster lines M and M+Nwhere M and N are integers and N is even. In the case where the spacingbetween the jets is not appropriate (e.g. not even), it is alwayspossible to scan only appropriate raster lines (e.g. those associatedwith every other jet) in a first pass and then to expose the remainingscan lines in one or more subsequent passes. As the width of depositionmay be significantly wider than the raster line spacing, other preferredembodiments might not be based on the skipping of every other scan lineon a first pass, but instead be based on the selection of scan lines fordeposition (i.e. exposing) on the first pass such that the lines ofdeposited material do not directly contact each other and then fillingin any skipped raster lines on one or more subsequent exposures.

This first alternative interlacing technique can be fully orapproximately implemented even when the adjacent jets areinappropriately positioned for the desired scan line resolution (i.e.the jet positions and scan line resolution are such that an even numberof raster lines exist between the line scanned by one of the jets andthe line scanned by an adjacent jet). This may be accomplished in atleast three ways: 1) each jet is used to scan every other raster linebetween its initial position and the position of the line initiallyformed by the adjacent jet except at least two adjacent raster lines tobe scanned by each jet will be left unexposed until at least a secondpass when the remaining raster lines will be exposed; 2) each jet isused to scan every other raster line until it also scans the raster lineadjacent to the first line scanned by the adjacent jet whereafter theremaining unexposed lines will be selectively exposed in a second pass;and/or 3) only every other jet is used in the scanning process therebyensuring that an odd number of raster lines exist between any twoadjacent jets. In these embodiments, as well as the previousembodiments, it is preferable to expose alternating lines for the wholelayer prior to beginning a second pass to expose the intermediate lines;however it is possible to complete the exposure of all scan linesbetween the starting points of some or all of the adjacent jets prior tomaking even a first pass over other portions of the layer.

Numerous other interlacing embodiments will apparent to those ofordinary skill in the art who study this disclosure. For example,interlacing with higher numbers of passes can be used or interlacingwherein some contact occurs between lines exposed on a first pass. Ofcourse any combination of interlacing with the previously describedrandomization techniques could also be used. Further exposure of asubsequent layer may change the order of scanning the various sets oflines and/or the scanning directions of the lines themselves (e.g.reverse the order of scanning of the first, second, and higher ordersets). Further embodiments might involve the completion of interlacingexposures for a first layer while exposing regions during formation ofone or more subsequent layers.

Drop Location Interlacing:

As with scan line interlacing, object formation may utilize droplocation interlacing along individual scan lines. In this case, eachscan line would be exposed by at least two passes wherein a first passwould expose a number of drop locations and, whereafter, on one or moresubsequent passes, the remaining drop locations would be exposed. As atwo step (i.e. pass) example, on a first pass every other drop sitewould be exposed while on a second pass the intermediate drop siteswould be exposed. This situation is depicted in FIGS. 12a and 12 b. FIG.12a depicts four scanning lines each with 9 drop locations wherein everyother drop location is to be exposed on a first pass while FIG. 12bdepicts the same lines and locations but instead depicts that onlycomplementary drop locations are to be exposed on a second pass. As asecond two step example every third site may be exposed on a first passwhile on a second pass both the intermediate sites, there between, wouldbe exposed. As a three step example, a first pass might expose everyfifth site beginning with the first site, then on a second pass everyfifth site would be exposed beginning with the third site, and finallyon a third pass every other site would be exposed beginning with thesecond site.

As with all other embodiments disclosed herein, the embodiments of thissection are combinable with the other embodiments disclosed herein.

In these interlacing techniques, successive scan lines may be exposedusing different or shifted interlacing patterns so that two dimensionalinterlacing patterns may be developed (offset pixelling could also beused). For example, a two step interlacing pattern may be used on eachscan line wherein the starting points on successive lines are shifted byone pixel such that a checkerboard first pass pattern is formed. FIGS.13a and 13 b illustrate this example. FIG. 13a depicts the first passcheckerboard pattern while FIG. 13b depicts the complementarycheckerboard pattern that is exposed on a second pass.

As with scan line interlacing, drop location interlacing may completeall passes over single lines prior to exposing subsequent lines thoughit is preferred that all lines be exposed with each pass prior toinitiating subsequent passes over partially exposed lines. Furthermore,completion of all passes over portions of single lines may be achievedprior to initiating exposure over remaining portions of those lines.

A third interlacing technique involves feature sensitive interlacing. Inthis technique the order in which a given drop site is exposed dependson the geometry of the immediate cross-section alone or on multiplecross-section geometries. Feature sensitive interlacing may involve oneor both of scan line interlacing and drop location interlacing. Forexample, in a single layer embodiment one may determine the boundaryregions of the cross-sections and ensure that the boundary zones areexposed on a first pass. Some interior portions of the cross-sectionmight also be exposed on the first pass or alternatively exposure of allinterior portions may be delayed until one or more subsequent passes aremade. For example, the interior portions may be exposed using acheckerboard interlacing pattern on a first pass in combination with allboundary regions also being exposed on the first pass. Then on a secondpass the remaining interior portions would be exposed. It is alsopossible that a wide boundary width could be defined for exposure on afirst pass so that more than a one-drop site width border may be placedaround the cross-section prior to performing subsequent passes. Thiswide boundary region might be implemented using erosion routines such asthose described above in association with Droplet Width Compensation. Asan additional alternative, one may focus on ensuring that only one ofscan line boundary sites or drop location boundary sites (boundariesalong lines in the secondary scanning direction) are exposed on thefirst pass. As a further alternative, internal regions may be exposed inwhole or in part prior to dispensing material in boundary regions. It isbelieved that dispensing boundary regions first might lead to improvedbuild-up in the vertical direction and that exposing boundary regionslast might lead to improved horizontal accuracy of the object. An evenfurther alternative might involve the dispensing of a near boundaryregion initially, followed by the dispensing of deeper internal regionsof the cross-section and finally followed by dispensing of the outercross-sectional boundary itself.

Examples of a multi-cross-sectional feature sensitive interlacingtechnique might involve initially exposing those locations which formpart of the present cross-section but which were boundary or solidinternal object regions on the previous cross-section. The boundary andsolid internal regions on the previous cross-section might includeboundary regions and solid internal regions of support structures aswell as object structures. In using this embodiment deposition in atleast critical (i.e. important) down-facing object regions does notoccur on the first pass unless those down-facing regions are actuallysupported by a structure of some nature (e.g. a support column directlybelow). In one or more subsequent exposures, material is dispensed toform unsupported down-facing features. Since the deposition width istypically wider than the pixel width, it is more likely that a dropletwhich is dispensed to land at a pixel location adjacent to previouslydispensed material on that cross-section, the droplet will strike andhopefully adhere to the neighboring deposited material as opposed tocontinue falling downward to a cross-section below that for which is wasintended. Furthermore, since in preferred embodiments support structuresare typically no more than one pixel in separation, when exposure ofunsupported down-facing regions occur the dispensed material will morelikely be wedged between material already dispensed on the present layeras opposed to being wedged between material dispensed on a previouslayer. However, since droplet diameter is typically less than depositiondiameter (i.e. impacted droplet diameter) and since it may be smallerthan pixel width, material deposited at an adjacent pixel location maynot sufficiently extend into the path of a falling droplet so as toensure a collision and stopping of the particle.

In another preferred embodiment, the drop locations would be shifted bya fraction of a pixel width (preferably approximately ½ a pixel width)along the main and/or secondary scanning directions (preferably both)when dispensing unsupported down-facing regions and preferably adjacentregions such that a droplet is more likely to be at least partiallysupported by previously dispensed material than if droplets weredeposited in perfect alignment. It is preferred that droplets overpartially unsupported regions be dispensed in a subsequent pass fromthose dispensed over fully supported regions. However, it is possible torely solely on the overlap with the previous cross-section (and not anyadditional benefit associated with adhesion to material previouslydispensed on the given cross-section) in ensuring reasonable verticalplacement of the droplets in at partially unsupported regions. In thisembodiment at least the support regions (e.g. columns) on the currentlayer would not be shifted. This ensures that registration from layer tolayer occurs. It is further preferred that wide gaps be closed byprogressively working deposition locations inward (i.e. multistage) fromsupported sides of the gap using multiple passes over the cross-section,wherein each pass is partially offset from the immediately precedingpass to ensure adequate overlap of droplets so as to limit any materialplacement beyond the required vertical level. Further, in one preferredembodiment, Simultaneous Multiple Layer Curing Techniques, as describedin U.S. Pat. No. 5,999,184, are used in order to offset criticaldown-facing data up one or more layers so that upon deposition materialforming the down-facing layer will be located at the correct level.

An example of this multistage horizontally and vertically offsetembodiment using a ½ pixel horizontal offset and 1 layer thicknessvertical offset is shown in FIGS. 23a-23 h. FIG. 23a depicts a side viewof an object 120 to be formed. FIG. 23b depicts object 120 as it wouldnormally be divided into layers 122, 124, 126, 128, and 130. FIG. 23cdepicts object 120 as it is to be divided into layers 122, 124, 126,128′, and 130′. Layer 128′ is different from 128 in that the down-facingportion of the layer has been removed as it is anticipated that it willbe created during deposition of the material on the next layer using aseries of successively offset exposures. Layer 130′ is similar to layer130 except that a different deposition pattern might be used in itsformation. FIG. 23d again depicts layers 122, 124, 126 and 128′ but inaddition depicts deposition locations, or pixel positions, 132-137 atwhich material may be deposited during formation of layer 130′. FIG. 23eis similar to FIG. 23d except that instead of showing drop locations132-137, drop locations 140-146 are shown. As can be seen from therelative positions of the drop locations, locations 132-137 and 140-146are offset from each other by ½ a pixel width. FIG. 23f depicts thedeposition pattern formed from a first pass of the print head in forminglayer 130′. Droplets 150, 151, 152, and 153 are deposited at droplocations 141, 145, 142, and 144, respectively. It can be seen thatdroplets 152 and 153 were only partially supported by layer 128′ andthat as a result it is assumed they will partially extend (as depicted)into the region originally belonging to layer 128. FIG. 23g depicts thedeposition pattern from the first pass in forming layer 130′ as well asadditional material deposited in a second pass. Region 160 and 162 weredeposited on the first pass and were represented in FIG. 23f as regions150, 152, 151 and 153. The deposition on the second pass occursaccording to the pixel arrangement depicted in FIG. 23d. Droplets 155and 156 are deposited at drop locations 132 and 137. In practice, thedispensing of droplets 155 and 156 would initially result in excessmaterial being applied over a portion of regions 160 and 162 but thisexcess would be trimmed off during the planarization process. Droplets157 and 158 are deposited at drop locations 134 and 135 but since theselocations are not fully bounded from below by material previouslydeposited, it is assumed that a portion of the material dispensed willextend downward into the region originally part of layer 128. The offsetdispensing of droplets 152, 153, 157 and 158 results in the formation ofthe down-facing portion of layer 128 which was removed from layer 128′.In a third and final pass, droplet 164 is deposited onto drop location143 to complete formation of layer 130′.

In other preferred embodiments various aspects to the above examplecould be changed. For example, the extension of material into lowerlayer regions (assumed to occur when droplets or drop locations are onlypartially supported) could take on values other than the 1 layerthickness extension described. The extension may be less than 1 layerthickness or at least different from an integral number of layerthickness. Maybe the extension would be an integral number of layerthicknesses (e.g. 2 to 5 layer thickness or more). In such a case, formost accurate formation, it would be desired to have the initial objectrepresentation transformed into a modified representation, as describedin U.S. Pat. No. 5,999,184, (either before or after generation ofcross-sectional data) so that when material is dispensed according tothe modified representation, the bottom of the down-facing feature isproperly located. Other variations might use geometry based deposition,in multiple passes, along with different offset values such as ¼ of apixel (so that ¾ of the drop zone would be unsupported) or ¾ of a pixel(such that only ¼ of the drop location would be unsupported). Thesedifferent offset amounts might lead to more control over the amounts ofextension into previous layer regions. Other variations might usedifferent deposition orders, different amounts of over printing, or evenquantities of deposition per droplet. Still other variations might notuse offset pixelling but instead would use higher resolution pixels,possibly in combination with deposition patterns yielding the rightdroplet density.

An additional interlacing technique combines: 1) feature sensitivity,and 2) selective direction of scanning when exposing object features. Inthis embodiment, cross-sectional geometry (e.g. cross-sectional boundaryinformation) from a current layer and possibly cross-sectional geometry(e.g. cross-sectional boundary information) from the immediatelypreceding layer would be used to determine what the direction ofscanning should be when exposing different regions of the cross-section.For example, when exposing the left most portion of a solid region of across-section it may be advantageous to be scanning the head (i.e. thejet used for exposing the line to be formed) from left to right if it isdesired that the droplet not bridge or not partially bridge any smallgaps. On the other hand, if it is desired that some bridging occur itmay be advantageous to ensure that scanning is in the oppositedirection. Similarly, when exposing the right most portion of a solidregion of the cross-section it may be advantageous to be scanning fromright to left (for no bridging) or from left to right (for bridging). Bycontrolling the scanning direction when depositing boundary regions itcan be ensured that horizontal momentum of the droplets either do notcontribute to bridging gaps or enhance the bridging of gaps.

An example of the non-bridging technique is illustrated in FIGS. 24a-24d. FIGS. 24a-d depict side views of two columns as being formed and ascut in an XZ plane. The Z-direction is perpendicular to the planes ofthe cross-sections and the X-direction is the main scanning direction.Reference numeral 108 indicates the cross-section being formed andreference numerals 100, 102, 104, and 106 refer to previously formedcross-sections. FIG. 24a depicts cross-section 108 with a broken line asno material deposition has taken place. FIG. 24b indicates that thescanning direction 110 is to the right and that droplets 112 aredeposited on the left most side of each column on a first pass. FIG. 24cindicates that the scanning direction 124 is to the left and thatdroplets 114 are deposited on the right most side of each column in asecond pass. FIG. 24d indicates that scanning can occur in eitherdirection 126 and that droplets 116, 118, 120, and 122 are deposited tocomplete the formation of the cross-section in a third pass. As opposedto the illustrated three pass embodiment, a two pass embodiment could beused wherein droplets 116, 118, 120, and 122 may have been deposited totheir respective locations during one or both of the first or secondpasses when droplets 112 and 114 were deposited.

It is anticipated that the object could be relatively reoriented (e.g.one or more rotations about the vertical axis) with respect to therelative scanning direction of the print head (i.e. jets) so that theedges of any desired cross-sectional features can be exposed whilerelatively moving the print head in a desired direction to enhance ordecrease the probability of bridging small gaps.

As noted above, if the orifice plate to working surface distance is toosmall, droplets will have an elongated shape (i.e. large aspect ratio)as they strike the working surface. In the case of building withelongated droplets, it is anticipated that the above indicated scanningdirections for depositing on edges of solid features might yieldopposite results from those indicated above. Other interlacingtechniques might involve bi-directional printing of adjacent rasterlines or non-adjacent raster lines.

The above-described building techniques can be applied to the formationof solid objects or in combination with other techniques to theformation of partially hollow or semi-solid objects. In an originaldesign of an object, portions of the object are supposed to be solid(i.e. be formed of solidified material) and portions are supposed to behollow (i.e. empty regions). In actuality these intended hollow (orvoid) regions that are not supposed to be part of the object, since bydefinition wherever there is object there is supposed to be material. Inthe context of the present invention a non-solid, hollow, or semi-solidobject, is an object built or to be built according to the teachings ofsome preferred embodiments wherein a portion of what should be solidobject has been removed. A typical example of this might be thehollowing out, partial hollowing out, or the honeycombing of what wasoriginally a solid structure of the object. These originally solidstructures are sometimes referred to as object walls regardless of theirspatial orientation. Some preferred build styles form completely solidobjects, while other build styles form solid surface regions of theobjects but hollowed out or partially hollowed out interior regions. Forexample, the interior portions of an object might be formed in acheckerboard, cross-hatched, hexagonal, tiled, or honeycombed manner(these and other build styles usefull herein, as implemented inphoto-based stereolithography are described in the above referencedpatents and applications). The above non-solid deposition patterns canbe considered internal object support structures. As such the othersupport structures described herein can also be used as internal objectsupport structures. Such non-solid objects would be lighter in weightthan their solid counterparts, they would use less material, they mighteven be formed more quickly depending on the details of the specificbuilding parameters, and they might be formed with less risk ofencountering heat dissipation problems since much less heated materialis deposited during their formation. These objects might be useful asinvestment casting patterns due to the decrease in the possibility ofcracking molds.

Temperature Control

Additional object formation embodiments involve the formation of theobject wherein the partially formed object is maintained within adesired temperature range as it is being formed or is at leastmaintained such that the differential in temperature across the part (orthe gradient of temperature difference) is small. If during objectformation, the different portions of the object are allowed to be atdifferent temperatures, the object will undergo a differential amount ofshrinkage as it is cooled to room temperature or as it is brought to itsuse temperature (the temperature at which it will be put to use). Thisdifferential in shrinkage could lead to the development of stresseswithin the object and associated distortions or even fractures of theobject. It is preferred that temperature differential remain within arange which is effective for maintaining object distortion within areasonable limit. The temperature differential across the object ispreferably maintained within a range of 20° C., more preferably within arange of 10° C. and even more preferably within a range of 5° C. andmost preferably within a range of 3° C. In any event, the desiredtemperature can be estimated by taking into consideration thecoefficient of thermal expansion of the material and the differential inshrinkage (or expansion) that would occur upon cooling (or heating) theformed object to a uniform temperature. If the differential in shrinkageresults in an error outside a desired tolerance range, the abovementioned ranges of temperatures can be adjusted.

In the formation of objects, the initial object data can be scaled totake into account dimensional changes in the object that will occur asthe object is cooled from its jetting temperature ( about 130° C. in thepreferred embodiment) to its solidification temperature (about 50°C.-80° C. with a peak DSC energy transfer temperature of about 56° C.)to its build temperature (about 40° C.-45° C.) and finally to its usetemperature (e.g. room temperature—about 25° C.). This scaling factorcould be used to expand the initial object design by an appropriatethermal shrinkage compensation factor such that it would beappropriately sized at its use temperature. It is further anticipatedthat one or more geometry dependent or at least axes dependent shrinkagefactors could be used to at least partially compensate critical regionsof the object for expected variations in object temperature during buildup.

The temperature of the previously formed lamina and the cooling rate ofthe lamina being formed have been found to be important parameters forthe formation of objects with reduced distortion and in particular withreduced curl distortion. Presently preferred materials undergo about 15%shrinkage when cooled from their solidification temperature to roomtemperature. This shrinkage provides a tremendous motivation force forcausing curl distortion, build up of internal stresses, and associatedpost processing distortions (these distortions are described with regardto photo-based stereolithography in the above referenced patents andapplications wherein many of the building techniques described thereincan be effectively utilized in the practice of SDM and TSL in view ofthe teaching found in the instant application). It has been found thatif the object build temperature and in particular if the temperature ofthe last formed layer is maintained at a temperature above roomtemperature during the build process, curl distortion will be reduced.It is preferred that the temperature of the entire partially formedobject be maintained above room temperature and, more particularly, thatits temperature remain within a tight tolerance band due to thedifferential shrinkage considerations discussed above.

For effective object formation, it is apparent that the buildtemperature of the partially formed object must be maintained below themelting point of the material. Additionally the build temperature mustbe maintained below a temperature that allows the solidified material tohave sufficient shear and compressional strength and even tensionalstrength (especially if sideways or upside down object formationembodiments are used) to allow the object to be accurately formed whileexperiencing the typical forces associated with the build process (e.g.inertial forces associated with accelerations the object willexperience, drag forces or vacuum forces associated with the planarizerand print head contacting or passing close to the object, air pressureforces associated with any air flow used to cool the object, andgravitational forces on the object due to its own weight). Some of theseforces are dependent on the mass of the object and increase with depthinto the part. Thus, a slight negative temperature gradient from higherto lower layers (i.e. decrease in temperature from most recently formedlayers to earliest formed layers) can supply increasing strength inneeded regions while simultaneously allowing the latest formed layer orlayers to be at a high enough temperature to result in minimal curl andother distortions. One might use a simple gravitational forcecalculation summed with an inertial force calculation for one or morepositions in the part (based on the mass of the part and the Y-directionacceleration it experiences) as an approximation of the minimum shearstrength needed from the solidified material. This in combination withan empirical determination of the variation of material shear strengthwith temperature can be used to estimate the approximate upper buildtemperature limit for any position in the object. Of course it ispreferred that additional considerations be taken into account,especially near the latest formed lamina of the object, since dynamicthermal effects occur at the interface of the partially formed objectand the material being dispensed that involve remelting phenomena andheat capacity phenomena which are dependent on object geometryparameters, temperature differentials, and cooling techniques. Thus, theactual overall maximum build temperature will probably be lower than theabove estimated amount.

On the other hand, as noted above, curl and other distortions can besignificantly reduced by building at elevated temperatures wherein thehigher the temperature the less the distortion. It is postulated thatthis reduction in distortion results from a combination of the materialsenhanced ability to flow at elevated temperatures and its lower abilityto support shear loads which allow some material redistribution to occurthereby reducing stress which causes distortion. It is furtherpostulated that working near, at, or preferably above any solid statephase change temperatures (e.g. crystallization temperature or glasstransition temperature) will result in the quickest and potentially mostsignificant reductions in stress and distortion. Since these phasechanges typically occur over a broad range, various levels of benefitare postulated to occur depending on where the working temperature is inwithin these ranges and the process time allowed. Melting temperaturesand/or solidification temperatures and solid state transitiontemperatures can be determined using Differential Scanning Calorimetry(DSC) techniques which in turn can be utilized in determiningappropriate build temperature ranges. Additionally, appropriate buildtemperature ranges can be determined empirically. It has been determinedthat some benefit can be gained by working at any temperature above roomtemperature and it is anticipated that the closer one moves to themelting temperature and/or solidification temperature the more thebenefit. Thus, the working temperature range might be set as apercentage of the distance along the temperature differential betweenroom temperature and melting or solidification temperature or roomtemperature and the temperature of estimated minimum shear strength.Alternatively, the working temperature may be selected to be atemperature for which the material has a certain percentage of its roomtemperature shear strength. For example it might be desired to set theworking (build) temperature such that the shear strength is 75%, 50%,25% or even 10% of its maximum room temperature value.

Surface Finish Enhancement

Additional building embodiments useful for enhancing object surfacefinish involve taking advantage of the aesthetically pleasing, up-facingsurfaces which result from the practice of preferred SDM techniques. Inthese embodiments the number of effective up-facing surfaces (e.g. theoverall area) is increased while the number of effective down-facingsurfaces is reduced from that defined by the original object design.This involves splitting the object into two or more pieces and changingthe orientation of the separated pieces such that as many criticalsurfaces as possible are made to be up-facing surfaces, verticalsurfaces or combined up-facing/vertical surfaces whereas no trulyexternal surfaces or only less critical surfaces remain as down-facingsurfaces. These separate object components are then built independentlyof one another, each with the proper orientation. Then supports areremoved and the resultant components combined by gluing, or the like,such that a complete object is formed primarily from up-facing andvertical surface regions. If rough surfaces are desired instead ofsmooth surfaces, the above technique can be used to ensure that criticalsurfaces are formed as down-facing surfaces. As an alternative theup-facing surfaces which are to be roughened can simply be formed withsupports extending therefrom.

An example of this building technique is illustrated in FIGS. 25a-e.FIG. 25a depicts the configuration of an object 60 to be formed usingSDM (i.e. the desired object design). If the object is formed directlyfrom this design, the object will be formed with both up-facing featuresor surfaces (50, 52, and 54) and down-features or surfaces (56 and 58).As discussed previously, the formation of down-facing features requiresthe prior formation of a support structure which acts as a workingsurface onto which material forming the down-facing features isdispensed. After object formation and removal of the supports, it hasbeen found that the down-facing surfaces are left with a rough andirregular surface finish. If it is desired that the down-facing surfacebe smooth, the object must undergo additional post-processing which mayrequire detailed sanding or filling.

FIG. 25b depicts the first step in the practice of the above technique.This first step involves splitting the original or desired object designinto two or more components. The splitting is performed so that allcritical features of the object can be formed as either verticalsurfaces or up-facing surfaces (preferably as up-facing surfaces andmore preferably as up-facing surfaces which do not have down-facingsurfaces above them so that supports will not be formed which start fromand mar the up-facing surfaces). Additional details about supportformation and issues associated therewith will be described furtherhereinafter. In the present example, all surfaces 50, 52, 54, 56 and 58are considered to be critical and should be formed as up-facingsurfaces.

FIG. 25b depicts object 60 being split into two portions 62 and 64.Portion 62 includes original outward facing features 50, 52, and 54 andnew or temporary outward facing features 72 and 74. Portion 64 includesoriginal or desired outward facing features 56 and 58 and new ortemporary outward facing features 72′ and 74′.

FIG. 25c depicts the preferred orientation (right side up) of portion 62during formation so that surfaces 50, 52 and 54 are formed as up-facingfeatures. FIG. 25d depicts the preferred orientation (upside down) ofportion 64 during formation so that surfaces 56 and 58 are formed asup-facing features. After formation of each portion 62 and 64 thesupports are removed and temporary pairs of surfaces 72 & 72′, and 74 &74′ are prepared for mating. FIG. 25e depicts the joining of portions 62and 64 to form object 60 wherein all critical outward facing portions(i.e. original surfaces 50, 52, 54, 56 and 58) have good surface finish.

Additional Build Styles

Other building styles might include one or more of the following: 1) theuse of higher resolution dispensing in the scanning directions; 2) theuse of a higher drop density per unit area in forming down-facing skinsurfaces than in forming interior regions of the object; 3) the use ofdown-facing skin regions which extend at least N layers (e.g., 5 to 10)above down-facing surfaces; 4) the use of a higher drop density per unitarea when forming up-facing skin surfaces than in forming interiorregions of the object; 5) use of up-facing skin regions which extend forat least N layers (e.g., 5 to 10) below an up-facing surface; 6) the useof higher drop density per unit area when forming boundary regions of anobject than when forming interior regions, boundary regions which extendat least L drop widths (e.g., 2 to 4) into the interior of an object;and 7) forming interior regions of the object through raster scanningand boundary regions through vector scanning.

Support Styles

The next portion of the application is primarily directed to supportformation. It should be appreciated, however, that as supports areformed from deposited material, all the aforementioned buildingtechniques are applicable to the support building process. Moreover, aswill be appreciated, all aspects of the support building process areapplicable to object building as well.

Support structures must serve several needs which may be opposing: 1)they preferably form a good working surface on which to build objectlamina and even successive support lamina; 2) they are preferably easilyremovable from the down-facing surfaces they support; 3) if they startfrom an up-facing surface of the object, they are preferably easilyremovable therefrom; 4) when removed, the supports preferably cause onlyminimal damage to down-facing and up-facing surfaces and preferably haveat least a tolerable to good surface finish on those surfaces; 5) theypreferably build up at a reasonable rate per cross-section in thevertical direction (e.g. Z-direction); 6) they are preferably formedusing a minimal number of passes per layer; and 7) their formation ispreferably reliable. A number of different support styles have beendeveloped or proposed which achieve different balances between theseneeds.

To optimize building speed, vertical accumulation is important and, assuch, it is desirable to have supports build up at approximately thesame rate as the object. In particular, it is preferred that thevertical accumulation of supports (e.g., from a single pass per layer)be at least as great as a desired layer thickness set by the use of theplanarizer. The closer the support accumulation is to that of objectaccumulation, the thicker the useable layer and the less material thatwill be removed during planarization which thereby increases theefficiency of the building process. For a given material and apparatus,the vertical build up of material from different support and buildstyles can be empirically determined, as described previously, bybuilding test parts for each deposition style or pattern using differentlayer thicknesses (planarization levels) and thereafter measuring theparts to determine when the build up of material lagged behind theanticipated thickness as dictated by the number of layers deposited andthe expected layer thickness. From this information one can either setthe layer thickness (planarization level) to an appropriate amount for adesired combination of build and support styles or one can set therequired support and build styles necessary to achieve the desired layerthickness.

Some preferred support style embodiments emphasize speed of formation,maintain easy removal, but leave rough surface finish in regions wheresupports have been removed. This support style involves the formation ofsolid columns which are separated by small gaps. In particular, in apreferred system, data is supplied at 300 pixels per inch in both the Xand Y directions and the object and supports are formed using four timesID overprinting in the X direction (main scanning direction). Each layerof supports includes three-by-three pixels zones where support materialis to be dispensed with the columns separated by two pixels zones of nopixel defined deposition along the main scanning direction (X-direction)and one pixel zone of no pixel defined deposition in the secondaryscanning direction (Y-direction). The data situation defining thesepixel zones is depicted in FIG. 15a. The “X's” in the figure depictpixels which contain droplet data while the “O's” in the figure depictpixels which contain “no droplet” data. Squares 50 have been inscribedaround the “X” zones so as to highlight the shape of the depositionzones. However, due to the ID overprinting in the X-direction, the twopixel gaps are actually narrowed considerably (by almost one pixelwidth) when actual deposition occurs. Thus, the actual resulting patternof deposition more closely approximates 4 by 3 pixel width (12-14 milsby 9-10 mils) columns, though with rounded corners, which are separatedby 1 pixel width gap in both X and Y (3.3 mils). This situation isapproximately depicted in FIG. 18.

In the practice of building objects it has been found that supports ofthe above configuration accumulate at approximately the same rate as theobject and thus a single pass of the head over each drop site can beused for forming both supports and object on each layer. It has alsobeen found that the above support structure is easily separable from theobject but that a poor down-facing surface finish results. Therefore, interms of building speed, the above style is preferred, but in terms ofsurface finish, significant room for improvement remains.

A variant involves using multiple passes of the dispensing head to forma support portion of a cross-section. Another alternative involvesperiodically dispensing an extra support cross-section in order toequalize vertical material accumulation between supports and the object.

Another variant involves allowing support formation to lag behind objectformation by one or more layers to eliminate or minimize planarizationproblems that can occur in the case where fragile supports are beingbuilt. The problem is that the planarizer can cause these supports todistort if support portions of a cross-section are dispensed during thesame pass or passes as the corresponding object portion of thecross-section. By allowing a lag of one or more layers to occur,excessive contact between the supports and the planarizer can beavoided, and it is anticipated that the resultant distortion of thesupports will be minimized.

Other column-like support structures are possible including columns ofdifferent dimensions or shapes. For example, data formatting andoverprinting techniques could be combined to produce physical columns ofapproximately a 3 by 3 pixel size (9-10 mils by 9-10 mils), 2-by-3 or3-by-2 pixel size (these may result in less vertical accumulation),2-by-2 (6-7 mils by 6-7 mils) pixel size (probable loss in verticalaccumulation rate), 4 by 4 (12-14 mils by 12-14 mils) pixel size (may bemore difficult to remove and cause further damage to object surfaces),or even larger sizes. Other cross-sectionally shaped columns may also beused. These might include more circularly shaped structures (e.g.octogonal or hexagonal), cross-like structures, structures withdifferent length to width aspect ratios, or combinations of structuresthat can be intermixed.

Other alternatives might include offsetting alternate support columns inone or both of the main and subscanning directions. For example, everyother support column could be offset in the secondary scanning directionby ½ the separation between columns. This is depicted in FIG. 19. Widerspacing of support columns is possible, particularly if some technique,such as arch or branching supports are used to narrow the gap betweenthe support columns prior to encountering a down-facing surface of theobject. Two examples of arch-like supports are depicted in FIGS. 21a and21 b wherein different amounts of pixel offsetting (or at least dropplacement control) are used).

Branching Supports:

As described at several locations herein above, some preferredembodiments utilize supports that may be described as branchingsupports. The arch-type supports discussed above are an example of atype of branch support. Branching or branch-type supports are supportstructures that are built such that portions of some lamina extendoutward in a cantilever manner from solidified regions on theimmediately preceding lamina. These outward extensions may be based onidentical (i.e. fixed) pixel positions from layer to layer.Alternatively these outward extensions may be based on fractional pixelwidth shifts in pixel positions between some or all layers. Furtheralternatives may be based on changing pixel patterns between some or alllayers. Some embodiments of branching supports produce more individualsupport structures at a surface to be supported than the number ofsupport structures from which the branching supports originated at alower layer.

In addition to the various embodiments disclosed previously (which inessence can be considered branching supports), FIGS. 28a, 28 b, 29 a-e,30 a-m, 31 a-c, 32 a-d depict additional examples of preferred branchingsupport structures. FIG. 28a depicts a side view of column supports 504,506 & 508 starting at surface 500 and working up toward surface 502.These column supports are connected one to another by branching elements510, 512, 514 and 516. FIG. 28b depicts a side view of an embodiment ofbranching type supports that work up from surface 500 toward surface502. The supports are shown to branch every two layers. In this twodimensional view, some branching appears to occur in a two pathfork-like pattern while other branches simply branch out along a singlepath. The same support structure depicted in FIG. 28b is looked at froma different view in FIGS. 31a-c and 32 a-d.

Other preferred branching patterns are illustrated in the example ofFIGS. 29a-e. FIGS. 29a-e depict top views of successive branchingcross-sections for a single support tree that uses X only and Y onlybranches and results in a total of four support branches from a singlesupport trunk. FIG. 29a depicts a single support structure that will bebranched into a plurality of structures. This single support structuremay be called the “trunk” of the support tree or structure. As will bemade clear below, for ease of data manipulation, the trunk can beconsidered to consist of four separate but identical components whichmaintain their separate identity, but may be Booleaned together to yieldthe scanning pattern for any given layer. Of course in practice a realregion to be supported might require a plurality of these trunk elementsappropriately spaced from each other.

FIG. 29b depicts a first branching in the X direction. As with the otherFigures to follow, the hatched solid regions, as depicted, represent thedeposition regions for the instant cross-section whereas the region(s)depicted with dashed lines represent the immediately proceeding branch.This way of depicting the deposition regions is done to make theregistration between branches clear. This first branching may occurafter one or more trunk layers are formed. As with other branches to bedescribed herein after in association with this figure and other figuresto follow, branching may extend the dispensed material out fromsupported regions by a fraction of a pixel, a full pixel, or multiplepixels depending on the drawing order used, the pixel width as comparedto the drop width, the number of identical layers to be formed above thepresent layer (which can compensate for imperfections in the presentlayer), ability of the material to be partially unsupported, and thelike. As with some of the other branches, to be discussed herein after,this branching can be looked at as a two way branch (i.e. one way in thepositive X direction and the other way in the negative X-direction) oras a one-way branch of two or more initially overlapped components. Aswill be seen from the description to follow, this first branch may beconsidered a one-way branching of four initial components wherein twocomponents follow each branching direction. The actual deposition ofmaterial from these four components may be based on a Boolean union ofthe components so that multiple depositions over overlapping regions areavoided.

FIG. 29c depicts the next branching of the tree wherein this branchingmay initially occur one or more layers after the branching depicted inFIG. 29b. This branching of object components occurs in the samedirections as seen in FIG. 29b.

FIG. 29d depicts two branchings in the Y-direction of each of the twobranches depicted in FIG. 29c. In concept, this may again be considereda single branching in the Y direction of separate components. Thebranching depicted in FIG. 29d is the first branch which begins theseparation process of all four components.

FIG. 29e depicts a final branch for this example embodiment wherein anadditional Y-direction branch of each component is made. These finalbranches can be used to support an object surface as appropriate. If anobject surface is located several layers above these final branches, thestructures (e.g. columns) of FIG. 29e can be extended until the objectsurface is encountered. If the object surface is not at the same levelfor all four branches the individual columns or portions of columns canbe extended as necessary. This extension of support height is similar toother preferred column support embodiments discussed herein and caninclude the use of bridge layers and the like. Of course if differentconfigurations (e.g. shapes, positions, and the like) of the four columnbranched support is desired, modifications (e.g. modifications tobranching order, branching directions, extension amounts, number oflayers between branches, and the like) to the depicted embodiment can bemade and will be apparent to one of skill in the art in view of theteachings herein. The support trunk depicted in FIG. 29a may initiallybe formed on a previous object cross-section or initial substrate.Alternatively, the trunk may begin on top of another support structuresuch as that depicted in FIG. 28a. Furthermore, if multiple trees are tobe used, branching of the trees may or may not begin on the same layerand may or may not result in each branch being formed after the samenumber of layers. Selection of where to beginning branching and when tomake successive branches thereafter, may be based on the geometry of theobject to be formed. It may be desirable to have the final branchingpattern achieved, for a particular tree, several layers before firstencountering a surface to be supported (e.g. down-facing objectsurface).

The branching routines performed in association with the exampleembodiment illustrated in FIGS. 29a- 29 e may outlined in the followingtable:

Component #1 Component #2 Component #3 Component #4 Build withoutbranching for a desired number of layers (FIG. 29a) Branch in the +XBranch in the +X Branch in the −X Branch in the −X direction by desireddirection by desired direction by desired direction by desired amount Aamount A amount A amount A (FIG. 29b) (FIG. 29b) (FIG. 29b) (FIG. 29b)Build without branching for a desired number of layers Branch in the +XBranch in the +X Branch in the −X Branch in the −X direction by desireddirection by desired direction by desired direction by desired amount Aamount A amount A amount A (FIG. 29c) (FIG. 29c) (FIG 29c) (FIG. 29c)Build without branching for a desired number of layers Branch in the +YBranch in the −Y Branch in the +Y Branch in the −Y direction by adesired by a desired direction by a desired direction by a desiredamount A amount A amount A amount A (FIG. 29d) (FIG. 29d) (FIG 29d)(FIG. 29d) uz,1/24 Build without branching for a desired number oflayers Branch in the +Y Branch in the −Y Branch in the +Y Branch in the−Y direction by a desired direction by a desired direction by a desireddirection by a desired amount A amount A amount A amount A Build withoutbranching until a new support style is implemented or until a surface ofthe object is encountered

As desired, the various parameters outlined in the above table can bemodified. For example the Branching amounts where taken as an amount“A”. As appropriate, this amount can vary with different branchinglevels or it can even vary for different components during the samebranching level.

FIGS. 30a-30 m depict an analogous branching support embodiment to thatof FIGS. 29a-29 e with the exception that the single trunk depicted inFIG. 30a will give rise to 16 branches as indicated in FIG. 30m. Forease of understanding and possibly implementation, the trunk shown inFIG. 30a can be considered as consisting of 16 individual but identicalcomponents. Again, the offset is performed along only one of either theX or the Y directions during a given branching operation for a givencomponent. All the considerations noted above in describing FIGS. 29a-ecan be applied to the example embodiment depicted in these Figures aswell as the example embodiments to follow.

FIGS. 31a-c depicts an additional example embodiment wherein a singletrunk, as depicted in FIG. 31a, is branched into four elements, asdepicted in FIG. 31c. This embodiment differs from that in FIGS. 29a-29c in that branching occurs simultaneously in both the X and Ydirections. As illustrated, the extent of branching is the same in boththe X and Y directions but this extent of branching could be variedbetween these directions.

FIGS. 32a-32 d continues the embodiment depicted in FIGS. 31a-31 c toyield 16 separate branched supports. These Figures further illustratethe Structure depicted in FIG. 28b wherein two layers for each branchare depicted.

In other preferred embodiments other branching patterns are possible.For example, instead of yielding rectangular arrays of branched supportsfrom individual trunks, as depicted in the above described examples,hexagonal arrays, triangular arrays, semi-circular arrays, or the likemay be formed. If the achieved patterns do not fit nicely together, itmay be desirable to use a mixture of patterns which are alternated in anappropriate fashion to give a good fitting or meshing of the finalsupport structures such that a down-facing surface can be adequatelysupported. Other preferred embodiments may use multiple trunks forsupporting single groups of branching supports.

It is anticipated that these branching support embodiments might yieldbetter down-facing surface than achieved with some of the otherpreferred embodiments since it is believed that the final supportstructures that contact the object will be more uniformly spaced. Asnoted above, the branched support embodiments described herein might bea part of a larger support structure or hybrid support structure. Othermodifications to the above embodiments will be apparent to one of skillin the art after studying the teachings herein.

If the geometry and direction sensitive interlacing techniques describedabove are used it may be possible to build smaller diameter and/or moreclosely spaced structures to provide a better working surface whilestill providing reasonable vertical accumulation rates.

In the preferred embodiment, deposited drop diameter is approximatelythe same as the preferred pixel diameter (about 2.9-3.4 mils). Ingeneral, however, the pixel separation between supports (e.g. separationbetween support columns) is less critical than the separation relativeto the falling drop diameter (e.g. 2 mils) and impacted (or deposited)drop diameter. Preferably the horizontal spacing between supports (e.g.support columns) is less than 6 drop diameters on the layer immediatelypreceding the layer containing the down-facing surface to be supported.More preferably, the spacing is less than 3 falling drop diameters, andmost preferably, the spacing is less than 1 to 2 falling drop diameters.

It has been found useful to include periodic bridging elements betweenthe support columns to limit their ability to shift from their desiredXY positions as they grow in height. Typically the smaller the diameterof the support columns the more often bridging elements or layers areneeded. These bridging elements may extend one or more layers in height.In the preferred embodiment, it has been found that a single layer (1-2mils) of bridging elements is not completely effective and that morethan five layers (5-10 mils) makes the overall support structure toorigid. Thus, when using the preferred 3 by 3 pixel supports, bridginglayers are preferably between 2 layers (2-4 mils) and 5 layers (5-10mils) in height and most preferably 3 layers (3-6 mils) in height.Furthermore, it has been found that the bridging layers are preferablyrepeated every 75 mils to 2 inches, more preferably every 100 to 300mils, and most preferably every 100 to 200 mils. For use with othermaterials, building parameters, or building conditions, formation andanalysis of test parts can be used to determine the effective bridgethickness and separations thicknesses.

When bridging layers are periodically used they may bind all supportcolumns together or they may bind only a portion of them togetherwherein the other columns were bound on a previous use of bridging orwill be bound on a subsequent use of bridging. In other words, thebridging elements may form a solid plane of deposited material oralternatively they may form only a partially solid plane (e.g. acheckerboard pattern) which connects some of the columns together. Thesupport columns may or may not be shifted from their previous XYpositions when they are restarted after formation of bridging layers.

Another preferred support structure which emphasizes easy removal andgood down-facing surface finish over speed of object production is knownas a checkerboard support. The cross-sectional configuration of thissupport structure is depicted in FIG. 14. Along each raster line,deposition occurs using every other pixel (300 pixels/inch) and inadjacent raster lines the deposition pixels are shifted along the lineby one pixel width. One preferred version of this support does not useID overprinting, but can use DD overprinting or multiple exposures toincrease deposition per layer. Without DD overprinting or multipleexposures, the layer thickness when using this type of support in thepreferred embodiment is limited to under 0.4 to 0.5 mils, instead of theapproximately 1.3 mils obtainable with some preferred embodimentsdescribed previously. Instead of using DD overprinting or multipleexposures with these supports, it is possible to not use the preferredID overprinting of the object, and simply deposit material in thinnerlayers (e.g. 0.3 to 0.5 mils per layer). Overprinting of the object doesnot need to be utilized as the extra material would simply need to beremoved during the planarization step. Since raster scanning is used andsince the speed of forming a layer is the same with or withoutoverprinting, build styles according to these techniques areapproximately 3 to 4 times slower than equivalent build styles wherefour times overprinting are used. Though there is a significant increasein build time the improvement in surface finish may warrant its useunder certain circumstances.

When building checkerboard supports, regular use of bridging layers ispreferred (e.g. every 30 to 100 mils of z-height) to ensure columnintegrity. The bridging layers should comprise a sufficient number oflayers to ensure their effectiveness (e.g. about the same thickness ofthe bridging layers discussed above). A drop-on/drop-off checkerboardpattern (in terms of drop width) is where the solidified elements are 1drop wide (deposition width), and spacing between the center points ofsuccessive elements is greater than 1 drop width but less than 2 dropwidths.

Line supports (in terms of drop width) comprise line elements which areapproximately one impacted droplet diameter in width, where the spacingbetween elements tangential to the orientation of the lines is less than1 drop width (i.e. overlapping), while the spacing between elementsperpendicular to the line orientation is greater than 1 drop width.Preferably, the spacing between elements perpendicular to the lineorientation is also less than 2 drop widths.

N-by-N column supports (in terms of pixels) are N-on, preferably one ortwo-off in the main scan direction, and N-on, and preferably 1-off inthe index direction. The width of the columns and spacing therebetweencan be calculated based on a knowledge of the pixel spacing, the dropdiameter and any overprinting used. The preferred spacing betweendeposited material in adjacent columns is under one to two dropletdiameters.

Another possible support style involves the use of solid or periodicallybroken lines which are preferably less than 3 pixels wide (less than 10mils) and more preferably 1 to 2 pixels or less in width (less than 3.3to 6.6 mils) and are separated by 1 to 2 pixels or less of undepositedmaterial (less than 3.3 to 6.6 mils). These supports may run along themain scanning directions, secondary scanning directions, or otherdirections. Another type of support is curved line supports which followthe boundary of an object. Alternatively, the support pattern can differat different areas of the cross-section. It can also be displaced fromthe boundary of the object by N pixels (or drop widths) in the scandirection, or M pixels (or drop widths) in the index direction.

Some other alternatives involve building supports from a differentmaterial than used to form the surface or boundary regions of theobject. Other alternatives might use a different support material onlyon one or more of the layers adjacent to the object.

Hybrid Supports

Further types of support structures useful for Selective DepositionModeling are Hybrid Supports. In its simplest sense, a hybrid support isa support structure that includes at least two different types ofsupport structures. Preferably, the structures used in a hybrid supportvary depending on the height of the support and, more particularly, thestructure at any given point may depend on the distance from that pointto an up-facing and/or down-facing surface of the object. In otherwords, the support structures are tailored to the most appropriatestructure based on the distance to the object. In an exemplaryembodiment, the support pattern is changed when the point is located apredetermined number of layers (e.g., 4 to 9) below a down-facingsurface. In another, the drop density per unit area or drop densityratio (defined as the drops to non-drops per unit area ratio) of thesupports is decreased as a down-facing surface is approached. In avariant of these embodiments, one or more layers of shelving (orintermediate) layers are used when transitioning from higher to lowerdrop density ratio support structures.

In still another exemplary embodiment, the drop density ratio isincreased as an up-facing surface is left (e.g., 4 or more layers awayfrom an up-facing surface). In an optional variant of this embodiment,one or more layers of shelving (intermediate) layers are used whentransitioning from lower to higher drop density ratio supportstructures. It is also conceivable that support structures could varynot just based on vertical distance from the object but also based onhorizontal distance as well. For example, when horizontally borderingthe object, a different type of support may be useful than when somedistance away from the object.

An example Hybrid support is depicted from the side in FIG. 20. Asshown, the structure extends from surface 23, which may be the buildingplatform, or which may be an up-facing surface of the object beingbuilt, to support down-facing surface 24. As depicted, the supportstructure consists of five components: (1) thin, fiber-like columns 25which contact surface 23 (if surface 23 is not an up-facing surface ofthe object this component of the support structure can be eliminated);(2) more massive columns 26 situated on top of the fiber-like columns25; (3) intermediate layers 27 (i.e. a final bridging layer); (4) thin,fiber-like columns 28 situated on top of the intermediate layers andwhich directly contact down-facing surface 24; and (5) bridging layers29 which are used to fuse two or more of the massive columns togetherand which are distributed at various places amongst the columns 26.

The thin columns 25 and 28 are both 1 pixel in cross-section (3.3×3.3mils) and form a “checkerboard” pattern as shown in FIG. 14a. The resultis a series of thin, fiber-like columns which are spaced by 1 pixel fromadjacent columns, and which easily separate from surfaces 23 and 24.These are equivalent to the checkerboard supports discussed above. Basedon the one-pixel on, one-pixel off deposition pattern of these supportsthe drop density ratio is approximately 1. If the support does not starton an up-facing surface of the object columns 25 can be skipped.

Columns 25 and 28 should be between 3 mils and 15 mils in height andpreferably about 4-6 mils in height. The height should be held to aminimum since it is desired that these supports be used in combinationwith an object which is being formed with 4 times ID overprinting andsince when using a single pass on these support structures withoutoverprinting they accumulate at a much slower rate than the object. Onthe other hand, it is desired that these supports have some height sincethe needlelike elements tend to melt down when the down-facing surfaceof the object is dispensed onto them.

Columns 26 are 3×3 pixels in cross-section (9.9 mils ×9.9 mils), and arespaced 2 pixels from adjacent columns in the scanning direction, and 1pixel from adjacent columns in the index direction. These columnsupports are equivalent to the most preferred supports discussed above.As discussed above, the primary reason for the extra space in the mainscanning direction is the fact that these supports will receive 4 timesoverprinting. The cross-sectional pattern formed by these columns isshown in FIGS. 15 and 18. The result is a series of columns more massivethan fiber-like columns 25 and 28.

These columns, unlike the others, can be arbitrarily tall. The reason isthat the larger cross-sections of these columns allow the columns togrow at about the same rate as the part itself (about 1.3 mils/layer).As previously discussed, it is preferred that bridges 29 be used to fuseadjacent ones of columns 26 together periodically to prevent “wandering”of these columns which can occur after building up for some distance.The spacing of the bridges is preferably in the previously discussedrange.

The intermediate layers 27 represent an optional final layer of bridgingwhich can function as a transition between columns 26 and columns 28.The reason a transition layer is useful is that the columns 28 are aboutthe same size or smaller than the spaces between the columns 26, withthe result that without the transition layers, the columns 28 may fallinto these spaces. In one preferred approach, intermediate layers as awhole would not be used and instead careful placement of columns 28 ontop of columns 26 would occur or only the necessary portions ofintermediate layers 27 would be used.

Preferably, if used, these intermediate layers are of similar thicknessto that of the previously discussed bridging layers.

It should be appreciated that intermediate layers are not needed betweencolumns 25 and columns 26, because the columns 26 are larger incross-section than the spacing between the columns 25. Accordingly,these larger columns can be built directly on top of the smaller columnswithout the need of intermediate layers.

Other hybrid supports are possible that make other combinations with thepreviously described support elements. The hybrid and other supportstructures may also be used to form internal portions of objects.

Additional alternatives exist for building supports. For example, it isalso possible to build the support from a material which is differentfrom that used to build the part. Another possibility is to add a fluidsuch as water between the interstices of the above described supportstructures in order to provide additional support and also for aidingheat dissipation. In such an approach, it is advantageous to use a fluidthat has a greater density than the building material. That will givebuoyancy to the drops of building material that fall between theinterstices of the columns. The material should also be chosen such thatits surface energy is matched to that of the building material in orderto prevent a meniscus forming between the fluid and the columns. Anexample of such a material is a surfactant.

Another possibility is to shoot air jets upward between the intersticesof the columns. In this approach a heat dissipation effect and buoyancyare possible. Another possibility is to fill the interstices of areduced number of column supports (e.g. columns placed 0.1 to 1 inch ormore apart) with particles. Moreover, such particles could be formedfrom the building material by allowing or causing the droplets tosolidify before they reach the working surface (such as by increasingthe distance between the dispensing head and the working surface), or bycoating the droplets before they land with a material that sublimes,i.e., goes directly from a solid to a gas.

Supports preferably space the object from 50 to 300 mils from thesurface of the building platform. Alternatively, the object may bedirectly built on the platform. In this alternative, the platform may becovered with a flexible sheet material that will allow easy separationof the object from the rigid platform and then from the sheet material.An electric knife may be used to separate the supports from the platformin which case it is preferred that object be placed 150 to 300 milsabove the platform surface. A thin comb-like device with long teeth hasbeen found effective for removing the supports from the platform. Inthis case, the thickness of the device dictates the required spacingbetween the object and the platform, typically between 50 and 200 mils.The supports may be removed from the object by light rubbing, brushingor by use of a small probe device such as a dental tool.

Another variant involves incorporating the subject embodiments into anintegrated system, which includes a capability for automatic partremoval, and a cooling station. Other alternatives involve using alow-melting, point metal as a building material, a material filler, ordifferent materials on different raster lines or drop locations.

Further alternatives involve using larger drops for support buildingthan for part building. Another alternative involves the use of powderedsupports, which may be formed by allowing or causing the droplets tosolidify before they reach the working surface, as described above.

Other embodiments might build up objects based on differentmain-scanning direction orientations (e.g. Y or Z), other secondaryscanning direction orientations (e.g. X or Z) and other stackingorientations (e.g. X or Y). Other embodiments might use other absolutemovement schemes to achieved the desired relative movements between theobject and print head. For example in some embodiments absolute movementof the print head might occur in all three directions, while in otherembodiments absolute object movement might occur in allthree-directions. In still other embodiments, non-Cartesian movement ofthe print head or object might be used and jetting directions may varyfrom layer to layer or portion of layer to portion of layer.

Though some embodiments have been described under headings inserted inthe application, these embodiments should not be considered aspertaining only to the topic indicated by the header. Furthermore,though headers were used to enhance the readability of thisspecification, all disclosure relevant to the particular topic recitedby the header should not be considered as falling within those singlesections. All embodiments disclosed herein are useful separately or incombination with other embodiments disclosed herein.

While embodiments and applications of this invention have been shown anddescribed, it will be apparent to those skilled in the art that manymore modifications are possible without departing from the inventiveconcepts herein. The invention, therefore, is not to be restricted,except in the spirit of the appended claims.

APPENDIX A TABLES I-III Detailing preferred materials for use in somepreferred embodiments TABLE I describes the component formulations.COMPONENT A paraffin wax, melting point 60° C. B pure monomerhydrocarbon resin comprising a copolymer of α- methylstyrene, vinyltoluene;viscosity 1000 cps @ 130° C.; softening point 78-95° C. C mediumhard microcrystalline ester wax; viscosity 16 cps @ 100° C.; meltingpoint 78-86° C.; penetration 1.7 mm @ 25° C. D hard microcrystallinewax; viscosity 16 cps @ 100° C.; melting point 93° C.; penetration 0.55mm @ 25° C. E soft microcrystalline wax; viscosity 13 cps @ 100° C.;melting point 69° C.; penetration 2.9 mm @ 25° C. F ethylene-vinylacetate copolymer; viscosity 575 cps @ 140° C.; melting point 92° C. Gtetrakis[methylene (3,5-di-tert-butyl-4-hydroxyhydrocinnamate)]methane,an antioxidant; melting point 110-125° C. H dioctylphthalate (DOP), aplasticizer I dioctylterephthalate (DOTP), a plasticizer J2,6-tert-butyl-4-methylphenal, an antioxidant K diisononyl phthalate(DINP), a plasticizer L dye or coloring compound M methacrylateterminated polystyrene N free radical photoinitiator O polyethyleneoxide, average molecular weight 2000 P epoxy novolac oligomer Q catonicphotoinitiator R multifunctional acrylate

TABLE II-A Appendix A: TABLES I-III Detailing preferred materials foruse in some preferred embodiments TABLE II-A and II-B presentformulations of preferred materials for use in some preferredembodiments by component designation. Weight % COMPONENT Ex. 1 Ex. 2 Ex.3 Ex. 4 Ex. 5 Ex. 6 A 21 21 44 25 20 20 B 49 49 25 20 25 50 C 12 12 12 —— 12 D 5 5 6 10 5 5 E 5 5 6 20 20 5 F 4 4 2.3 20 25 4 G 2 2 — — — — H —2 — — — — I — — 2.3 2 2.5 2 J — — 2.3 3 2.5 2 K 2 — — — — — PROPERTIESViscosity @ 130 cps/° C. 22 22 7 20 28 24 ° C. Hardness shore D 28 26Impact Energy kJ/m² 1.4 2.2

TABLE II-B COMPONENT Ex. 7 Ex. 8 Ex. 9 A 21 M 51 C 12 D 5 E 5 F 5 N 1 1O 77 77 P 22 Q 1 R 22

TABLE III COMPONENT NAME SUPPLIER A Paraffin Allied Signal Inc.,Morristown, NJ B “PICOTEX LC” Hercules, Inc., Wilmington, DE C “X-22”Hoechst Celanese Corp., Somerville, NJ D “C-700” Petrolite Corp., Tulsa,OK E “ULTRAFLEX” Petrolite Corp., Tulsa, OK F “AC-400” Allied SignalInc., Morristown, NJ G “IRGANOX 1010” Ciba-Geigy Corp., Hawthorne, NY HDOTP Aldrich Chemical Co., Inc., Milwaukee, WI I DOP Aldrich ChemicalCo., Inc., Milwaukee, WI J “BHT” Aldrich Chemical Co., Inc., Milwaukee,WI K DINP Aristech Chemical Corp., Cleveland, OH M “13K-RC” SartomerCo., West Chester, PA N “IRGACURE 184” Ciba-Geigy Corp., Hawthorne, NY OPolyethelene Oxide Dow Chemicals, Midland, MI P “DEN 438” Dow Chemicals,Midland, MI Q “UVI 6974” Union Carbide Chemicals, Danbury, CT R “SR 399”Sartomer Co., West Chester, PA

What is claimed is:
 1. A method for rapid prototyping comprising:controllably dispensing a flowable material which is solidifiable uponbeing dispensed to form a three-dimensional object, the material beingdispensed to accumulate in a vertical direction at a desired rate in alayer-by-layer cross-section fashion on a support platform; supporting across-section of a three-dimensional object and providing a workingsurface for building a next object cross-section that accumulates in thevertical direction at the desired rate; passing a planarizer over theworking surface to smooth the working surface and establish a layerthickness for each cross-section; relatively displacing the dispenserand the working surface in at least two dimensions, comprising ascanning direction and an index direction; dispensing material over theworking surface in accordance with a selected style; and creating asupport structure for each cross-section, the support structureaccumulating in the vertical direction at about the desired rate.
 2. Themethod of claim 1 further comprising selectively dispensing material tocreate solid columns of support structure separated by gaps.
 3. Themethod of claim 1 wherein said style is a building style.
 4. The methodof claim 1 wherein said style is a support style.
 5. The method of claim1 additionally comprising the step of forming support structures whichbranch out beyond material dispensed on an immediately preceding layerwherein the branching results in more support structures contacting adown-facing object surface than the number of support structures fromwhich the branching was initiated.
 6. The method of claim 1 additionallycomprising the step of directing droplets at a focal plane below a levelof an actual working surface for achieving a self-correctingaccumulation in a direction perpendicular to a plane of thecross-sections.
 7. The method of claim 1 additionally comprising thestep of directing a cooling gas onto the surface of a partially formedobject and the step of removing the cooling gas from the area above saidsurface.
 8. The method of claim 1 wherein the flowable materialcontrollably dispensed is the same material employed to build thethree-dimensional object and to create the support structure.
 9. Themethod of claim 1 further comprising using a first flowable material tobuild the three-dimensional object and a second material to create thesupport structure.
 10. The method of claim 1 further comprisingselectively dispensing material to create support structure selectedfrom the group consisting of solid columns, thin fiber-like columns,bridging layers, and branching supports.
 11. The method of claim 1further comprising solidifying the flowable material.
 12. The method ofclaim 11 further comprising solidifying the flowable material usingradiation.
 13. The method of claim 11 further comprising solidifying theflowable material by cooling.
 14. A method for rapid prototypingcomprising controllably dispensing a solidifiable flowable material toform a three-dimensional object, the material being dispensed toaccumulate in a vertical direction at a desired rate in a layer-by-layercross-section fashion on a support surface and establishing a workingsurface for building a next object cross-section; creating a supportstructure for each cross-section, the support structure accumulating inthe vertical direction at about the desired rate; passing a planarizerover the working surface to smooth the working surface and establish alayer thickness for each cross-section.
 15. The method of claim 14wherein the flowable material that is controllably dispensed is the samematerial employed to build the three-dimensional object and to createthe support structure.
 16. The method of claim 14 further comprisingusing a first flowable material to build the three-dimensional objectand a second material to create the support structure.
 17. The method ofclaim 14 further comprising selectively dispensing material to createsupport structure selected from the group consisting of solid columns,thin fiber-like columns, bridging layers, branching supports.
 18. Themethod of claim 14 further comprising solidifying the flowable material.19. The method of claim 18 further comprising solidifying the flowablematerial using radiation.
 20. The method of claim 18 further comprisingsolidifying the flowable material by cooling.
 21. The method of claim 14additionally comprising the step of forming support structures whichbranch out beyond material dispensed on an immediately preceding layerwherein the branching results in more support structures contacting adown-facing object surface than the number of support structures fromwhich the branching was initiated.
 22. The method of claim 14additionally comprising the step of directing droplets at a focal planebelow a level of an actual working surface for achieving aself-correcting accumulation in a direction perpendicular to a plane ofthe cross-sections.
 23. The method of claim 20 additionally comprisingthe step of directing a cooling gas onto the surface of a partiallyformed object and the step of removing the cooling gas from the areaabove said surface.